%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.19", %%% date = "20 October 2023", %%% time = "17:40:45 MDT", %%% filename = "ejp.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "06196 63362 296421 2908086", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Electronic %%% Journal of Probability", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE bibliography of %%% publications in the open-source journal, %%% Electronic Journal of Probability (CODEN %%% none, ISSN 1083-6489, ISSN-L 1083-6489) %%% published in collaboration with the Institute %%% of Mathematical Statistics. Publication %%% began at the University of Washington %%% (Seattle, WA, USA) with volume 1, number 1, %%% in 1996. There is only one volume per year, %%% but articles are available online as soon as %%% they have been accepted for publication. %%% %%% In 2016, journal hosting moved to Project %%% Euclid. %%% %%% The journal has Web sites at %%% %%% https://projecteuclid.org/euclid.ejp %%% http://ejp.ejpecp.org/ %%% http://www.math.washington.edu/~ejpecp/EJP/ %%% %%% There is also a companion journal for shorter %%% communications: it is covered in ecp.bib. %%% %%% At version 1.19, the year coverage looked %%% like this: %%% %%% 1996 ( 14) 2006 ( 50) 2016 ( 70) %%% 1997 ( 9) 2007 ( 58) 2017 ( 97) %%% 1998 ( 16) 2008 ( 76) 2018 ( 120) %%% 1999 ( 23) 2009 ( 94) 2019 ( 138) %%% 2000 ( 14) 2010 ( 73) 2020 ( 160) %%% 2001 ( 32) 2011 ( 92) 2021 ( 157) %%% 2002 ( 16) 2012 ( 107) 2022 ( 164) %%% 2003 ( 23) 2013 ( 109) 2023 ( 47) %%% 2004 ( 29) 2014 ( 122) %%% 2005 ( 46) 2015 ( 129) %%% %%% Article: 2085 %%% %%% Total entries: 2085 %%% %%% Data for this bibliography have been derived %%% primarily from data at the publisher Web %%% site, with contributions from the BibNet %%% Project and TeX User Group bibliography %%% archives, and the MathSciNet and zbMATH %%% databases. %%% %%% Numerous errors in the sources noted above %%% have been corrected. Spelling has been %%% verified with the UNIX spell and GNU ispell %%% programs using the exception dictionary %%% stored in the companion file with extension %%% .sok. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by the biblabel software %%% developed for the BibNet Project. %%% %%% In this bibliography, entries are sorted in %%% publication order, with the help of %%% ``bibsort -bypages''. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{ "\ifx \undefined \cprime \def \cprime {$'$}\fi" # "\ifx \undefined \flqq \def \flqq {\ifmmode \ll \else \leavevmode \raise 0.2ex \hbox{$\scriptscriptstyle \ll $}\fi}\fi" # "\ifx \undefined \frqq \def \frqq {\ifmmode \gg \else \leavevmode \raise 0.2ex \hbox{$\scriptscriptstyle \gg $}\fi}\fi" # "\ifx \undefined \k \let \k = \c \fi" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" # "\ifx \undefined \mathfrak \let \mathfrak = \mathcal \fi" # "\ifx \undefined \mathscr \def \mathscr #1{{\cal #1}}\fi" # "\ifx \undefined \text \def \text #1{{\hbox{\rm #1}}}\fi" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-nhfb = "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"} %%% ==================================================================== %%% Journal abbreviations: @String{j-ELECTRON-J-PROBAB = "Electronic Journal of Probability"} %%% ==================================================================== %%% Bibliography entries, sorted in publication order with %%% ``bibsort -byvolume'': @Article{Khoshnevisan:1996:LCS, author = "Davar Khoshnevisan", title = "{L{\'e}vy} classes and self-normalization", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "1:1--1:18", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-1", ISSN = "1083-6489", MRclass = "60F15 (60J15 60J45 60J55)", MRnumber = "1386293 (97h:60024)", MRreviewer = "Qi Man Shao", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1; http://www.math.washington.edu/~ejpecp/EjpVol1/paper1.abs.html", abstract = "We prove a Chung's law of the iterated logarithm for recurrent linear Markov processes. In order to attain this level of generality, our normalization is random. In particular, when the Markov process in question is a diffusion, we obtain the integral test corresponding to a law of the iterated logarithm due to Knight.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Self-normalization, Levy Classes", } @Article{Lawler:1996:HDC, author = "Gregory F. Lawler", title = "{Hausdorff} dimension of cut points for {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "2:1--2:20", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-2", ISSN = "1083-6489", MRclass = "60J65", MRnumber = "1386294 (97g:60111)", MRreviewer = "Paul McGill", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2", abstract = "Let $B$ be a Brownian motion in $ R^d$, $ d = 2, 3$. A time $ t \in [0, 1]$ is called a cut time for $ B[0, 1]$ if $ B[0, t) \cap B(t, 1] = \emptyset $. We show that the Hausdorff dimension of the set of cut times equals $ 1 - \zeta $, where $ \zeta = \zeta_d$ is the intersection exponent. The theorem, combined with known estimates on $ \zeta_3$, shows that the percolation dimension of Brownian motion (the minimal Hausdorff dimension of a subpath of a Brownian path) is strictly greater than one in $ R^3$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, Hausdorff dimension, cut points, intersection exponent", } @Article{Bass:1996:EEB, author = "Richard F. Bass and Krzysztof Burdzy", title = "Eigenvalue expansions for {Brownian} motion with an application to occupation times", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "3:1--3:19", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-3", ISSN = "1083-6489", MRclass = "60J65", MRnumber = "1386295 (97c:60201)", MRreviewer = "Zhong Xin Zhao", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3; http://www.math.washington.edu/~ejpecp/EjpVol1/paper3.abs.html", abstract = "Let $B$ be a Borel subset of $ R^d$ with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting $B$. Let $ A_1$ be the time spent by Brownian motion in a closed cone with vertex $0$ until time one. We show that $ \lim_{u \to 0} \log P^0 (A_1 < u) / \log u = 1 / \xi $ where $ \xi $ is defined in terms of the first eigenvalue of the Laplacian in a compact domain. Eigenvalues of the Laplacian in open and closed sets are compared.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, eigenfunction expansion, eigenvalues, arcsine law", } @Article{Pitman:1996:RDD, author = "Jim Pitman and Marc Yor", title = "Random Discrete Distributions Derived from Self-Similar Random Sets", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "4:1--4:28", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-4", ISSN = "1083-6489", MRclass = "60D05", MRnumber = "1386296 (98i:60010)", MRreviewer = "Bert Fristedt", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4", abstract = "A model is proposed for a decreasing sequence of random variables $ (V_1, V_2, \cdots) $ with $ \sum_n V_n = 1 $, which generalizes the Poisson--Dirichlet distribution and the distribution of ranked lengths of excursions of a Brownian motion or recurrent Bessel process. Let $ V_n $ be the length of the $n$ th longest component interval of $ [0, 1] \backslash Z$, where $Z$ is an a.s. non-empty random closed of $ (0, \infty)$ of Lebesgue measure $0$, and $Z$ is self-similar, i.e., $ c Z$ has the same distribution as $Z$ for every $ c > 0$. Then for $ 0 \leq a < b \leq 1$ the expected number of $n$'s such that $ V_n \in (a, b)$ equals $ \int_a^b v^{-1} F(d v)$ where the structural distribution $F$ is identical to the distribution of $ 1 - \sup (Z \cap [0, 1])$. Then $ F(d v) = f(v)d v$ where $ (1 - v) f(v)$ is a decreasing function of $v$, and every such probability distribution $F$ on $ [0, 1]$ can arise from this construction.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "interval partition, zero set, excursion lengths, regenerative set, structural distribution", } @Article{Seppalainen:1996:MMB, author = "Timo Sepp{\"a}l{\"a}inen", title = "A microscopic model for the {Burgers} equation and longest increasing subsequences", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "5:1--5:51", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-5", ISSN = "1083-6489", MRclass = "60K35 (35Q53 60C05 82C22)", MRnumber = "1386297 (97d:60162)", MRreviewer = "Shui Feng", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/5", abstract = "We introduce an interacting random process related to Ulam's problem, or finding the limit of the normalized longest increasing subsequence of a random permutation. The process describes the evolution of a configuration of sticks on the sites of the one-dimensional integer lattice. Our main result is a hydrodynamic scaling limit: The empirical stick profile converges to a weak solution of the inviscid Burgers equation under a scaling of lattice space and time. The stick process is also an alternative view of Hammersley's particle system that Aldous and Diaconis used to give a new solution to Ulam's problem. Along the way to the scaling limit we produce another independent solution to this question. The heart of the proof is that individual paths of the stochastic process evolve under a semigroup action which under the scaling turns into the corresponding action for the Burgers equation, known as the Lax formula. In a separate appendix we use the Lax formula to give an existence and uniqueness proof for scalar conservation laws with initial data given by a Radon measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Hydrodynamic scaling limit, Ulam's problem, Hammersley's process, nonlinear conservation law, the Burgers equation, the Lax formula", } @Article{Fleischmann:1996:TSA, author = "Klaus Fleischmann and Andreas Greven", title = "Time-Space Analysis of the Cluster-Formation in Interacting Diffusions", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "6:1--6:46", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-6", ISSN = "1083-6489", MRclass = "60K35 (60J60)", MRnumber = "1386298 (97e:60151)", MRreviewer = "Ingemar Kaj", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/6", abstract = "A countable system of linearly interacting diffusions on the interval [0, 1], indexed by a hierarchical group is investigated. A particular choice of the interactions guarantees that we are in the diffusive clustering regime, that is spatial clusters of components with values all close to 0 or all close to 1 grow in various different scales. We studied this phenomenon in [FG94]. In the present paper we analyze the evolution of single components and of clusters over time. First we focus on the time picture of a single component and find that components close to 0 or close to 1 at a late time have had this property for a large time of random order of magnitude, which nevertheless is small compared with the age of the system. The asymptotic distribution of the suitably scaled duration a component was close to a boundary point is calculated. Second we study the history of spatial 0- or 1-clusters by means of time scaled block averages and time-space-thinning procedures. The scaled age of a cluster is again of a random order of magnitude. Third, we construct a transformed Fisher--Wright tree, which (in the long-time limit) describes the structure of the space-time process associated with our system. All described phenomena are independent of the diffusion coefficient and occur for a large class of initial configurations (universality).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "interacting diffusion, clustering, infinite particle system, delayed coalescing random walk with immigration, transformed Fisher--Wright tree, low dimensional systems, ensemble of log-coalescents", } @Article{Bryc:1996:CMR, author = "W{\l}odzimierz Bryc", title = "Conditional Moment Representations for Dependent Random Variables", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "7:1--7:14", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-7", ISSN = "1083-6489", MRclass = "60A10 (60B99 60E15 62J12)", MRnumber = "1386299 (97j:60004)", MRreviewer = "M. M. Rao", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/7", abstract = "The question considered in this paper is which sequences of $p$-integrable random variables can be represented as conditional expectations of a fixed random variable with respect to a given sequence of sigma-fields. For finite families of sigma-fields, explicit inequality equivalent to solvability is stated; sufficient conditions are given for finite and infinite families of sigma-fields, and explicit expansions are presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "alternating conditional expectation, inverse problems, ACE", } @Article{Liao:1996:ASE, author = "Xiao Xin Liao and Xuerong Mao", title = "Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "8:1--8:16", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-8", ISSN = "1083-6489", MRclass = "60H10 (34K40)", MRnumber = "1386300 (97d:60100)", MRreviewer = "Tom{\'a}s Caraballo", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/8", abstract = "In this paper we shall discuss the almost sure exponential stability for a neutral differential difference equation with damped stochastic perturbations of the form $ d[x(t) - G(x(t - \tau))] = f(t, x(t), x(t - \tau))d t + \sigma (t) d w(t) $. Several interesting examples are also given for illustration. It should be pointed out that our results are even new in the case when $ \sigma (t) \equiv 0 $, i.e., for deterministic neutral differential difference equations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "neutral equations, stochastic perturbation, exponential martingale inequality, Borel--Cantelli's lemma, Lyapunov exponent", } @Article{Roberts:1996:QBC, author = "Gareth O. Roberts and Jeffrey S. Rosenthal", title = "Quantitative bounds for convergence rates of continuous time {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "9:1--9:21", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-9", ISSN = "1083-6489", MRclass = "60J25", MRnumber = "1423462 (97k:60198)", MRreviewer = "Mu Fa Chen", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/9", abstract = "We develop quantitative bounds on rates of convergence for continuous-time Markov processes on general state spaces. Our methods involve coupling and shift-coupling, and make use of minorization and drift conditions. In particular, we use auxiliary coupling to establish the existence of small (or pseudo-small) sets. We apply our method to some diffusion examples. We are motivated by interest in the use of Langevin diffusions for Monte Carlo simulation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov process, rates of convergence, coupling, shift-coupling, minorization condition, drift condition", } @Article{Arous:1996:MTD, author = "G{\'e}rard Ben Arous and Rapha{\"e}l Cerf", title = "Metastability of the Three Dimensional {Ising} Model on a Torus at Very Low Temperatures", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "10:1--10:55", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-10", ISSN = "1083-6489", MRclass = "82C44 (05B50 60J10 60K35)", MRnumber = "1423463 (98a:82086)", MRreviewer = "Peter Eichelsbacher", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/10; http://www.math.washington.edu/~ejpecp/EjpVol1/paper10.abs.html", abstract = "We study the metastability of the stochastic three dimensional Ising model on a finite torus under a small positive magnetic field at very low temperatures.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Ising, metastability, droplet, Freidlin--Wentzell theory, large deviations", } @Article{Bass:1996:USE, author = "Richard F. Bass", title = "Uniqueness for the {Skorokhod} equation with normal reflection in {Lipschitz} domains", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "11:1--11:29", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-11", ISSN = "1083-6489", MRclass = "60J60 (60J50)", MRnumber = "1423464 (98d:60155)", MRreviewer = "Zhen-Qing Chen", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/11; http://www.math.washington.edu/~ejpecp/EjpVol1/paper11.abs.html", abstract = "We consider the Skorokhod equation\par $$ d X_t = d W_t + (1 / 2) \nu (X_t), d L_t $$ in a domain $D$, where $ W_t$ is Brownian motion in $ R^d$, $ \nu $ is the inward pointing normal vector on the boundary of $D$, and $ L_t$ is the local time on the boundary. The solution to this equation is reflecting Brownian motion in $D$. In this paper we show that in Lipschitz domains the solution to the Skorokhod equation is unique in law.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Lipschitz domains, Neumann problem, reflecting Brownian motion, mixed boundary problem, Skorokhod equation, weak uniqueness, uniqueness in law, submartingale problem", } @Article{Gravner:1996:PTT, author = "Janko Gravner", title = "Percolation Times in Two-Dimensional Models For Excitable Media", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "12:1--12:19", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-12", ISSN = "1083-6489", MRclass = "60K35 (90C27)", MRnumber = "1423465 (98c:60141)", MRreviewer = "Rahul Roy", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/12", abstract = "The three-color {\em Greenberg--Hastings model (GHM) } is a simple cellular automaton model for an excitable medium. Each site on the lattice $ Z^2 $ is initially assigned one of the states 0, 1 or 2. At each tick of a discrete--time clock, the configuration changes according to the following synchronous rule: changes $ 1 \to 2 $ and $ 2 \to 0 $ are automatic, while an $x$ in state 0 may either stay in the same state or change to 1, the latter possibility occurring iff there is at least one representative of state 1 in the local neighborhood of $x$. Starting from a product measure with just 1's and 0's such dynamics quickly die out (turn into 0's), but not before 1's manage to form infinite connected sets. A very precise description of this ``transient percolation'' phenomenon can be obtained when the neighborhood of $x$ consists of 8 nearest points, the case first investigated by S. Fraser and R. Kapral. In addition, first percolation times for related monotone models are addressed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "additive growth dynamics, excitable media, Greenberg--Hastings model, percolation", } @Article{Lawler:1996:CTS, author = "Gregory F. Lawler", title = "Cut Times for Simple Random Walk", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "13:1--13:24", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-13", ISSN = "1083-6489", MRclass = "60J15 (60J65)", MRnumber = "1423466 (97i:60088)", MRreviewer = "Thomas Polaski", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/13", abstract = "Let $ S(n) $ be a simple random walk taking values in $ Z^d $. A time $n$ is called a cut time if \par $$ S[0, n] \cap S[n + 1, \infty) = \emptyset . $$ We show that in three dimensions the number of cut times less than $n$ grows like $ n^{1 - \zeta }$ where $ \zeta = \zeta_d$ is the intersection exponent. As part of the proof we show that in two or three dimensions \par $$ P(S[0, n] \cap S[n + 1, 2 n] = \emptyset) \sim n^{- \zeta }, $$ where $ \sim $ denotes that each side is bounded by a constant times the other side.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walk, cut points, intersection exponent", } @Article{Dawson:1996:MST, author = "Donald A. Dawson and Andreas Greven", title = "Multiple Space-Time Scale Analysis For Interacting Branching Models", journal = j-ELECTRON-J-PROBAB, volume = "1", pages = "14:1--14:84", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v1-14", ISSN = "1083-6489", MRclass = "60K35 (60J80)", MRnumber = "1423467 (97m:60148)", MRreviewer = "Jean Vaillancourt", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/14", abstract = "We study a class of systems of countably many linearly interacting diffusions whose components take values in $ [0, \inf) $ and which in particular includes the case of interacting (via migration) systems of Feller's continuous state branching diffusions. The components are labelled by a hierarchical group. The longterm behaviour of this system is analysed by considering space-time renormalised systems in a combination of slow and fast time scales and in the limit as an interaction parameter goes to infinity. This leads to a new perspective on the large scale behaviour (in space and time) of critical branching systems in both the persistent and non-persistent cases and including that of the associated historical process. Furthermore we obtain an example for a rigorous renormalization analysis.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching processes, interacting diffusions, super random walk, renormalization, historical processes", } @Article{Takacs:1997:RWP, author = "Christiane Takacs", title = "Random Walk on Periodic Trees", journal = j-ELECTRON-J-PROBAB, volume = "2", pages = "1:1--1:16", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v2-15", ISSN = "1083-6489", MRclass = "60J15", MRnumber = "1436761 (97m:60101)", MRreviewer = "Jochen Geiger", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/15", abstract = "Following Lyons (1990, Random Walks and Percolation on Trees) we define a periodic tree, restate its branching number and consider a biased random walk on it. In the case of a transient walk, we describe the walk-invariant random periodic tree and calculate the asymptotic rate of escape (speed) of the walk. This is achieved by exploiting the connections between random walks and electric networks.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Trees, Random Walk, Speed", } @Article{Rosen:1997:LIL, author = "Jay Rosen", title = "Laws of the Iterated Logarithm for Triple Intersections of Three Dimensional Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "2", pages = "2:1--2:32", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v2-16", ISSN = "1083-6489", MRclass = "60F15 (60J15)", MRnumber = "1444245 (98d:60063)", MRreviewer = "Karl Grill", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/16", abstract = "Let $ X = X_n, X' = X'_n $, and $ X'' = X''_n $, $ n \geq 1 $, be three independent copies of a symmetric three dimensional random walk with $ E(|X_1 |^2 \log_+ |X_1 |) $ finite. In this paper we study the asymptotics of $ I_n $, the number of triple intersections up to step $n$ of the paths of $ X, X'$ and $ X''$ as $n$ goes to infinity. Our main result says that the limsup of $ I_n$ divided by $ \log (n) \log_3 (n)$ is equal to $ 1 \over \pi |Q|$, a.s., where $Q$ denotes the covariance matrix of $ X_1$. A similar result holds for $ J_n$, the number of points in the triple intersection of the ranges of $ X, X'$ and $ X''$ up to step $n$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walks, intersections", } @Article{Abraham:1997:APB, author = "Romain Abraham and Wendelin Werner", title = "Avoiding-probabilities for {Brownian} snakes and super-{Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "2", pages = "3:1--3:27", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v2-17", ISSN = "1083-6489", MRclass = "60J25 (60G57)", MRnumber = "1447333 (98j:60100)", MRreviewer = "John Verzani", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/17", abstract = "We investigate the asymptotic behaviour of the probability that a normalized $d$-dimensional Brownian snake (for instance when the life-time process is an excursion of height 1) avoids 0 when starting at distance $ \varepsilon $ from the origin. In particular we show that when $ \varepsilon $ tends to 0, this probability respectively behaves (up to multiplicative constants) like $ \varepsilon^4$, $ \varepsilon^{2 \sqrt {2}}$ and $ \varepsilon^{(\sqrt {17} - 1) / 2}$, when $ d = 1$, $ d = 2$ and $ d = 3$. Analogous results are derived for super-Brownian motion started from $ \delta_x$ (conditioned to survive until some time) when the modulus of $x$ tends to 0.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian snakes, superprocesses, non-linear differential equations", } @Article{Jakubowski:1997:NST, author = "Adam Jakubowski", title = "A non-{Skorohod} topology on the {Skorohod} space", journal = j-ELECTRON-J-PROBAB, volume = "2", pages = "4:1--4:21", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v2-18", ISSN = "1083-6489", MRclass = "60F17 (60B05 60B10 60G17)", MRnumber = "1475862 (98k:60046)", MRreviewer = "Ireneusz Szyszkowski", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/18", abstract = "A new topology (called $S$) is defined on the space $D$ of functions $ x \colon [0, 1] \to R^1$ which are right-continuous and admit limits from the left at each $ t > 0$. Although $S$ cannot be metricized, it is quite natural and shares many useful properties with the traditional Skorohod's topologies $ J_1$ and $ M_1$. In particular, on the space $ P(D)$ of laws of stochastic processes with trajectories in $D$ the topology $S$ induces a sequential topology for which both the direct and the converse Prokhorov's theorems are valid, the a.s. Skorohod representation for subsequences exists and finite dimensional convergence outside a countable set holds.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Skorohod space, Skorohod representation, convergence in distribution, sequential spaces, semimartingales", } @Article{Arcones:1997:LIL, author = "Miguel A. Arcones", title = "The Law of the Iterated Logarithm for a Triangular Array of Empirical Processes", journal = j-ELECTRON-J-PROBAB, volume = "2", pages = "5:1--5:39", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v2-19", ISSN = "1083-6489", MRclass = "60B12 (60F15)", MRnumber = "1475863 (98k:60006)", MRreviewer = "Winfried Stute", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/19", abstract = "We study the compact law of the iterated logarithm for a certain type of triangular arrays of empirical processes, appearing in statistics (M-estimators, regression, density estimation, etc). We give necessary and sufficient conditions for the law of the iterated logarithm of these processes of the type of conditions used in Ledoux and Talagrand (1991): convergence in probability, tail conditions and total boundedness of the parameter space with respect to certain pseudometric. As an application, we consider the law of the iterated logarithm for a class of density estimators. We obtain the order of the optimal window for the law of the iterated logarithm of density estimators. We also consider the compact law of the iterated logarithm for kernel density estimators when they have large deviations similar to those of a Poisson process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Empirical process, law of the iterated logarithm, triangular array, density estimation", } @Article{Bertoin:1997:CPV, author = "Jean Bertoin", title = "{Cauchy}'s Principal Value of Local Times of {L{\'e}vy} Processes with no Negative Jumps via Continuous Branching Processes", journal = j-ELECTRON-J-PROBAB, volume = "2", pages = "6:1--6:12", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v2-20", ISSN = "1083-6489", MRclass = "60J30 (60J55)", MRnumber = "1475864 (99b:60120)", MRreviewer = "N. H. Bingham", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/20", abstract = "Let $X$ be a recurrent L{\'e}vy process with no negative jumps and $n$ the measure of its excursions away from $0$. Using Lamperti's connection that links $X$ to a continuous state branching process, we determine the joint distribution under $n$ of the variables $ C^+_T = \int_0^T{\bf 1}_{{X_s > 0}}X_s^{-1}d s$ and $ C^-_T = \int_0^T{\bf 1}_{{X_s < 0}}|X_s|^{-1}d s$, where $T$ denotes the duration of the excursion. This provides a new insight on an identity of Fitzsimmons and Getoor on the Hilbert transform of the local times of $X$. Further results in the same vein are also discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cauchy's principal value, L{\'e}vy process with no negative jumps, branching process", } @Article{Mueller:1997:FWR, author = "Carl Mueller and Roger Tribe", title = "Finite Width For a Random Stationary Interface", journal = j-ELECTRON-J-PROBAB, volume = "2", pages = "7:1--7:27", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v2-21", ISSN = "1083-6489", MRclass = "60H15 (35R60)", MRnumber = "1485116 (99g:60106)", MRreviewer = "Richard B. Sowers", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/21", abstract = "We study the asymptotic shape of the solution $ u(t, x) \in [0, 1] $ to a one-dimensional heat equation with a multiplicative white noise term. At time zero the solution is an interface, that is $ u(0, x) $ is 0 for all large positive $x$ and $ u(0, x)$ is 1 for all large negative $x$. The special form of the noise term preserves this property at all times $ t \geq 0$. The main result is that, in contrast to the deterministic heat equation, the width of the interface remains stochastically bounded.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic partial differential equations, duality, travelling waves, white noise", } @Article{Kager:1997:GOS, author = "Gerald Kager and Michael Scheutzow", title = "Generation of One-Sided Random Dynamical Systems by Stochastic Differential Equations", journal = j-ELECTRON-J-PROBAB, volume = "2", pages = "8:1--8:17", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v2-22", ISSN = "1083-6489", MRclass = "60H10 (28D10 34C35 34F05)", MRnumber = "1485117 (99b:60080)", MRreviewer = "Xue Rong Mao", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/22", abstract = "Let $Z$ be an $ R^m$-valued semimartingale with stationary increments which is realized as a helix over a filtered metric dynamical system $S$. Consider a stochastic differential equation with Lipschitz coefficients which is driven by $Z$. We show that its solution semiflow $ \phi $ has a version for which $ \varphi (t, \omega) = \phi (0, t, \omega)$ is a cocycle and therefore ($S$, $ \varphi $) is a random dynamical system. Our results generalize previous results which required $Z$ to be continuous. We also address the case of local Lipschitz coefficients with possible blow-up in finite time. Our abstract perfection theorems are designed to cover also potential applications to infinite dimensional equations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic differential equation, random dynamical system, cocycle, perfection", } @Article{Chaleyat-Maurel:1997:PPD, author = "Mireille Chaleyat-Maurel and David Nualart", title = "Points of Positive Density for Smooth Functionals", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "1:1--1:8", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-23", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/23", abstract = "In this paper we show that the set of points where the density of a Wiener functional is strictly positive is an open connected set, assuming some regularity conditions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Nondegenerate smooth Wiener functionals, Malliavin calculus, Support of the law", } @Article{Chaleyat-Maurel:1998:PPD, author = "Mireille Chaleyat-Maurel and David Nualart", title = "Points of positive density for smooth functionals", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "1:1--1:8", year = "1998", CODEN = "????", ISSN = "1083-6489", MRclass = "60H07", MRnumber = "1487202 (99b:60072)", MRreviewer = "Shi Zan Fang", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://www.math.washington.edu/~ejpecp/EjpVol3/paper1.abs.html", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hitczenko:1998:HCM, author = "Pawe{\l} Hitczenko and Stanis{\l}aw Kwapie{\'n} and Wenbo V. Li and Gideon Schechtman and Thomas Schlumprecht and Joel Zinn", title = "Hypercontractivity and Comparison of Moments of Iterated Maxima and Minima of Independent Random Variables", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "2:1--2:26", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-24", ISSN = "1083-6489", MRclass = "60B11 (52A21 60E07 60E15 60G15)", MRnumber = "1491527 (99k:60008)", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/24", abstract = "We provide necessary and sufficient conditions for hypercontractivity of the minima of nonnegative, i.i.d. random variables and of both the maxima of minima and the minima of maxima for such r.v.'s. It turns out that the idea of hypercontractivity for minima is closely related to small ball probabilities and Gaussian correlation inequalities.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "hypercontractivity, comparison of moments, iterated maxima and minima, Gaussian correlation inequalities, small ball probabilities", } @Article{Aldous:1998:EBM, author = "David Aldous and Vlada Limic", title = "The Entrance Boundary of the Multiplicative Coalescent", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "3:1--3:59", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-25", ISSN = "1083-6489", MRclass = "60J50 (60J75)", MRnumber = "1491528 (99d:60086)", MRreviewer = "M. G. Shur", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/25", abstract = "The multiplicative coalescent $ X(t) $ is a $ l^2$-valued Markov process representing coalescence of clusters of mass, where each pair of clusters merges at rate proportional to product of masses. From random graph asymptotics it is known (Aldous (1997)) that there exists a {\em standard} version of this process starting with infinitesimally small clusters at time $ - \infty $. In this paper, stochastic calculus techniques are used to describe all versions $ (X(t); - \infty < t < \infty)$ of the multiplicative coalescent. Roughly, an extreme version is specified by translation and scale parameters, and a vector $ c \in l^3$ of relative sizes of large clusters at time $ - \infty $. Such a version may be characterized in three ways: via its $ t \to - \infty $ behavior, via a representation of the marginal distribution $ X(t)$ in terms of excursion-lengths of a L{\'e}vy-type process, or via a weak limit of processes derived from the standard version via a ``coloring'' construction.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov process, entrance boundary, excursion, L{\'e}vy process, random graph, stochastic coalescent, weak convergence", } @Article{Cranston:1998:GEU, author = "Michael Cranston and Yves {Le Jan}", title = "Geometric Evolution Under Isotropic Stochastic Flow", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "4:1--4:36", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-26", ISSN = "1083-6489", MRclass = "60H10 (60J60)", MRnumber = "1610230 (99c:60115)", MRreviewer = "R{\'e}mi L{\'e}andre", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/26", abstract = "Consider an embedded hypersurface $M$ in $ R^3$. For $ \Phi_t$ a stochastic flow of differomorphisms on $ R^3$ and $ x \in M$, set $ x_t = \Phi_t (x)$ and $ M_t = \Phi_t (M)$. In this paper we will assume $ \Phi_t$ is an isotropic (to be defined below) measure preserving flow and give an explicit description by SDE's of the evolution of the Gauss and mean curvatures, of $ M_t$ at $ x_t$. If $ \lambda_1 (t)$ and $ \lambda_2 (t)$ are the principal curvatures of $ M_t$ at $ x_t$ then the vector of mean curvature and Gauss curvature, $ (\lambda_1 (t) + \lambda_2 (t)$, $ \lambda_1 (t) \lambda_2 (t))$, is a recurrent diffusion. Neither curvature by itself is a diffusion. In a separate addendum we treat the case of $M$ an embedded codimension one submanifold of $ R^n$. In this case, there are $ n - 1$ principal curvatures $ \lambda_1 (t), \ldots {}, \lambda_{n - 1} (t)$. If $ P_k, k = 1, \dots, n - 1$ are the elementary symmetric polynomials in $ \lambda_1, \ldots {}, \lambda_{n - 1}$, then the vector $ (P_1 (\lambda_1 (t), \ldots {}, \lambda_{n - 1} (t)), \ldots {}, P_{n - 1} (\lambda_1 (t), \ldots {}, \lambda_{n - 1} (t))$ is a diffusion and we compute the generator explicitly. Again no projection of this diffusion onto lower dimensions is a diffusion. Our geometric study of isotropic stochastic flows is a natural offshoot of earlier works by Baxendale and Harris (1986), LeJan (1985, 1991) and Harris (1981).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic flows, Lyapunov exponents, principal curvatures", } @Article{Evans:1998:CLT, author = "Steven N. Evans and Edwin A. Perkins", title = "Collision Local Times, Historical Stochastic Calculus, and Competing Species", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "5:1--5:120", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-27", ISSN = "1083-6489", MRclass = "60G57 (60H99 60J55 60J80)", MRnumber = "1615329 (99h:60098)", MRreviewer = "Anton Wakolbinger", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/27", abstract = "Branching measure-valued diffusion models are investigated that can be regarded as pairs of historical Brownian motions modified by a competitive interaction mechanism under which individuals from each population have their longevity or fertility adversely affected by collisions with individuals from the other population. For 3 or fewer spatial dimensions, such processes are constructed using a new fixed-point technique as the unique solution of a strong equation driven by another pair of more explicitly constructible measure-valued diffusions. This existence and uniqueness is used to establish well-posedness of the related martingale problem and hence the strong Markov property for solutions. Previous work of the authors has shown that in 4 or more dimensions models with the analogous definition do not exist.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "super-process, super-Brownian motion, interaction, local time, historical process, measure-valued Markov branching process, stochastic calculus, martingale measure, random measure", xxtitle = "Collision local times, historical stochastic calculus, and competing superprocesses", } @Article{Ferrari:1998:FSS, author = "P. A. Ferrari and L. R. G. Fontes", title = "Fluctuations of a Surface Submitted to a Random Average Process", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "6:1--6:34", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-28", ISSN = "1083-6489", MRclass = "60K35", MRnumber = "1624854 (99e:60214)", MRreviewer = "T. M. Liggett", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/28", abstract = "We consider a hypersurface of dimension $d$ imbedded in a $ d + 1$ dimensional space. For each $ x \in Z^d$, let $ \eta_t(x) \in R$ be the height of the surface at site $x$ at time $t$. At rate $1$ the $x$-th height is updated to a random convex combination of the heights of the `neighbors' of $x$. The distribution of the convex combination is translation invariant and does not depend on the heights. This motion, named the random average process (RAP), is one of the linear processes introduced by Liggett (1985). Special cases of RAP are a type of smoothing process (when the convex combination is deterministic) and the voter model (when the convex combination concentrates on one site chosen at random). We start the heights located on a hyperplane passing through the origin but different from the trivial one $ \eta (x) \equiv 0$. We show that, when the convex combination is neither deterministic nor concentrating on one site, the variance of the height at the origin at time $t$ is proportional to the number of returns to the origin of a symmetric random walk of dimension $d$. Under mild conditions on the distribution of the random convex combination, this gives variance of the order of $ t^{1 / 2}$ in dimension $ d = 1$, $ \log t$ in dimension $ d = 2$ and bounded in $t$ in dimensions $ d \ge 3$. We also show that for each initial hyperplane the process as seen from the height at the origin converges to an invariant measure on the hyper surfaces conserving the initial asymptotic slope. The height at the origin satisfies a central limit theorem. To obtain the results we use a corresponding probabilistic cellular automaton for which similar results are derived. This automaton corresponds to the product of (infinitely dimensional) independent random matrices whose rows are independent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random average process, random surfaces, product of random matrices, linear process, voter model, smoothing process", } @Article{Feyel:1998:ASS, author = "Denis Feyel and Arnaud {de La Pradelle}", title = "On the approximate solutions of the {Stratonovitch} equation", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "7:1--7:14", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-29", ISSN = "1083-6489", MRclass = "60H07 (60G17)", MRnumber = "1624858 (99j:60075)", MRreviewer = "Marco Ferrante", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/29", abstract = "We present new methods for proving the convergence of the classical approximations of the Stratonovitch equation. We especially make use of the fractional Liouville-valued Sobolev space $ W^{r, p}({\cal J}_{\alpha, p}) $. We then obtain a support theorem for the capacity $ c_{r, p} $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stratonovitch equations, Kolmogorov lemma, quasi-sure analysis", } @Article{Capinski:1998:MAS, author = "Marek Capi{\'n}ski and Nigel J. Cutland", title = "Measure attractors for stochastic {Navier--Stokes} equations", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "8:1--8:15", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-30", ISSN = "1083-6489", MRclass = "60H15 (35B40 35Q30 35R60)", MRnumber = "1637081 (99f:60115)", MRreviewer = "Wilfried Grecksch", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/30", abstract = "We show existence of measure attractors for 2-D stochastic Navier--Stokes equations with general multiplicative noise.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic Navier--Stokes equations, measure attractors", } @Article{Kurtz:1998:MPC, author = "Thomas G. Kurtz", title = "Martingale problems for conditional distributions of {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "9:1--9:29", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-31", ISSN = "1083-6489", MRclass = "60J25 (60G25 60G44 60J35)", MRnumber = "1637085 (99k:60186)", MRreviewer = "Amarjit Budhiraja", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/31", abstract = "Let $X$ be a Markov process with generator $A$ and let $ Y(t) = \gamma (X(t))$. The conditional distribution $ \pi_t$ of $ X(t)$ given $ \sigma (Y(s) \colon s \leq t)$ is characterized as a solution of a filtered martingale problem. As a consequence, we obtain a generator/martingale problem version of a result of Rogers and Pitman on Markov functions. Applications include uniqueness of filtering equations, exchangeability of the state distribution of vector-valued processes, verification of quasireversibility, and uniqueness for martingale problems for measure-valued processes. New results on the uniqueness of forward equations, needed in the proof of uniqueness for the filtered martingale problem are also presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "partial observation, conditional distribution, filtering, forward equation, martingale problem, Markov process, Markov function, quasireversibility, measure-valued process", } @Article{Kesten:1998:AAW, author = "Harry Kesten and Vladas Sidoravicius and Yu Zhang", title = "Almost All Words Are Seen In Critical Site Percolation On The Triangular Lattice", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "10:1--10:75", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-32", ISSN = "1083-6489", MRclass = "60K35", MRnumber = "1637089 (99j:60155)", MRreviewer = "Rahul Roy", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/32", abstract = "We consider critical site percolation on the triangular lattice, that is, we choose $ X(v) = 0 $ or 1 with probability 1/2 each, independently for all vertices $v$ of the triangular lattice. We say that a word $ (\xi_1, \xi_2, \dots) \in \{ 0, 1 \}^{\mathbb {N}}$ is seen in the percolation configuration if there exists a selfavoiding path $ (v_1, v_2, \dots)$ on the triangular lattice with $ X(v_i) = \xi_i, i \ge 1$. We prove that with probability 1 ``almost all'' words, as well as all periodic words, except the two words $ (1, 1, 1, \dots)$ and $ (0, 0, 0, \dots)$, are seen. ``Almost all'' words here means almost all with respect to the measure $ \mu_\beta $ under which the $ \xi_i$ are i.i.d. with $ \mu_\beta {\xi_i = 0} = 1 - \mu_\beta {\xi_i = 1} = \beta $ (for an arbitrary $ 0 < \beta < 1$).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Percolation, Triangular lattice", } @Article{Yoo:1998:USS, author = "Hyek Yoo", title = "On the unique solvability of some nonlinear stochastic {PDEs}", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "11:1--11:22", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-33", ISSN = "1083-6489", MRclass = "60H15 (35R60)", MRnumber = "1639464 (99h:60126)", MRreviewer = "Bohdan Maslowski", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/33", abstract = "The Cauchy problem for 1-dimensional nonlinear stochastic partial differential equations is studied. The uniqueness and existence of solutions in $ c H^2_p(T)$-space are proved.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic PDEs, Space of Bessel potentials, Embedding theorems", } @Article{Fitzsimmons:1998:MPI, author = "P. J. Fitzsimmons", title = "{Markov} processes with identical bridges", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "12:1--12:12", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-34", ISSN = "1083-6489", MRclass = "60J25 (60J35)", MRnumber = "1641066 (99h:60142)", MRreviewer = "Kyle Siegrist", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/34", abstract = "Let $X$ and $Y$ be time-homogeneous Markov processes with common state space $E$, and assume that the transition kernels of $X$ and $Y$ admit densities with respect to suitable reference measures. We show that if there is a time $ t > 0$ such that, for each $ x \in E$, the conditional distribution of $ (X_s)_{0 \le s \leq t}$, given $ X_0 = x = X_t$, coincides with the conditional distribution of $ (Y_s)_{0 \leq s \leq t}$, given $ Y_0 = x = Y_t$, then the infinitesimal generators of $X$ and $Y$ are related by $ L^Y f = \psi^{-1}L^X(\psi f) - \lambda f$, where $ \psi $ is an eigenfunction of $ L^X$ with eigenvalue $ \lambda \in {\bf R}$. Under an additional continuity hypothesis, the same conclusion obtains assuming merely that $X$ and $Y$ share a ``bridge'' law for one triple $ (x, t, y)$. Our work extends and clarifies a recent result of I. Benjamini and S. Lee.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bridge law, eigenfunction, transition density", } @Article{Davies:1998:LAE, author = "Ian M. Davies", title = "{Laplace} asymptotic expansions for {Gaussian} functional integrals", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "13:1--13:19", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-35", ISSN = "1083-6489", MRclass = "60H05 (41A60)", MRnumber = "1646472 (99i:60109)", MRreviewer = "Kun Soo Chang", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/35", abstract = "We obtain a Laplace asymptotic expansion, in orders of $ \lambda $, of\par $$ E^\rho_x \left \{ G(\lambda x) e^{- \lambda^{-2} F(\lambda x)} \right \} $$ the expectation being with respect to a Gaussian process. We extend a result of Pincus and build upon the previous work of Davies and Truman. Our methods differ from those of Ellis and Rosen in that we use the supremum norm to simplify the application of the result.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian processes, asymptotic expansions, functional integrals", } @Article{Csaki:1998:LFS, author = "Endre Cs{\'a}ki and Zhan Shi", title = "Large favourite sites of simple random walk and the {Wiener} process", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "14:1--14:31", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-36", ISSN = "1083-6489", MRclass = "60F15 (60G50 60J65)", MRnumber = "1646468 (2000d:60050)", MRreviewer = "Davar Khoshnevisan", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/36", abstract = "Let $ U(n) $ denote the most visited point by a simple symmetric random walk $ \{ S_k \}_{k \ge 0} $ in the first $n$ steps. It is known that $ U(n)$ and $ m a x_{0 \leq k \leq n} S_k$ satisfy the same law of the iterated logarithm, but have different upper functions (in the sense of P. L{\'e}vy). The distance between them however turns out to be transient. In this paper, we establish the exact rate of escape of this distance. The corresponding problem for the Wiener process is also studied.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Local time, favourite site, random walk, Wiener process", } @Article{Montgomery-Smith:1998:CRM, author = "Stephen Montgomery-Smith", title = "Concrete Representation of Martingales", journal = j-ELECTRON-J-PROBAB, volume = "3", pages = "15:1--15:15", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v3-37", ISSN = "1083-6489", MRclass = "60G42 (60G07 60H05)", MRnumber = "1658686 (99k:60116)", MRreviewer = "Dominique L{\'e}pingle", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/37", abstract = "Let $ (f_n) $ be a mean zero vector valued martingale sequence. Then there exist vector valued functions $ (d_n) $ from $ [0, 1]^n $ such that $ \int_0^1 d_n(x_1, \dots, x_n) \, d x_n = 0 $ for almost all $ x_1, \dots, x_{n - 1} $, and such that the law of $ (f_n) $ is the same as the law of $ (\sum_{k = 1}^n d_k(x_1, \dots, x_k)) $. Similar results for tangent sequences and sequences satisfying condition (C.I.) are presented. We also present a weaker version of a result of McConnell that provides a Skorohod like representation for vector valued martingales.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "martingale, concrete representation, tangent sequence, condition (C.I.), UMD, Skorohod representation", } @Article{Pak:1998:RWF, author = "Igor Pak", title = "Random Walks On Finite Groups With Few Random Generators", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "1:1--1:11", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-38", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/38", abstract = "Let $G$ be a finite group. Choose a set $S$ of size $k$ uniformly from $G$ and consider a lazy random walk on the corresponding Cayley graph. We show that for almost all choices of $S$ given $ k = 2 a \, \log_2 |G|$, $ a > 1$, this walk mixes in under $ m = 2 a \, \log \frac {a}{a - 1} \log |G|$ steps. A similar result was obtained earlier by Alon and Roichman and also by Dou and Hildebrand using a different techniques. We also prove that when sets are of size $ k = \log_2 |G| + O(\log \log |G|)$, $ m = O(\log^3 |G|)$ steps suffice for mixing of the corresponding symmetric lazy random walk. Finally, when $G$ is abelian we obtain better bounds in both cases.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random random walks on groups, random subproducts, probabilistic method, separation distance", } @Article{Pak:1999:RWF, author = "Igor Pak", title = "Random walks on finite groups with few random generators", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "1:1--1:11", year = "1999", CODEN = "????", ISSN = "1083-6489", MRclass = "60B15 (60G50)", MRnumber = "1663526 (2000a:60008)", MRreviewer = "Martin V. Hildebrand", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://www.math.washington.edu/~ejpecp/EjpVol4/paper1.abs.html", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Krylov:1999:AVF, author = "N. V. Krylov", title = "Approximating Value Functions for Controlled Degenerate Diffusion Processes by Using Piece-Wise Constant Policies", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "2:1--2:19", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-39", ISSN = "1083-6489", MRclass = "49L25 (35K65)", MRnumber = "1668597 (2000b:49056)", MRreviewer = "Martino Bardi", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/39", abstract = "It is shown that value functions for controlled degenerate diffusion processes can be approximated with error of order $ h^{1 / 3} $ by using policies which are constant on intervals $ [k h^2, (k + 1)h^2) $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bellman's equations, fully nonlinear equations", } @Article{Bressaud:1999:DCN, author = "Xavier Bressaud and Roberto Fern{\'a}ndez and Antonio Galves", title = "Decay of Correlations for Non-{H{\"o}lderian} Dynamics. {A} Coupling Approach", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "3:1--3:19", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-40", ISSN = "1083-6489", MRclass = "60G10 (28D05 37A25 37A50)", MRnumber = "1675304 (2000j:60049)", MRreviewer = "Bernard Schmitt", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/40", abstract = "We present an upper bound on the mixing rate of the equilibrium state of a dynamical system defined by the one-sided shift and a non H{\"o}lder potential of summable variations. The bound follows from an estimation of the relaxation speed of chains with complete connections with summable decay, which is obtained via a explicit coupling between pairs of chains with different histories.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dynamical systems, non-H{\"o}lder dynamics, m ixing rate, chains with complete connections, relaxation speed, coupling methods", } @Article{Dawson:1999:HIF, author = "Donald A. Dawson and Andreas Greven", title = "Hierarchically interacting {Fleming--Viot} processes with selection and mutation: multiple space time scale analysis and quasi-equilibria", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "4:1--4:81", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-41", ISSN = "1083-6489", MRclass = "60J70 (60K35 92D10 92D25)", MRnumber = "1670873 (2000e:60139)", MRreviewer = "Anton Wakolbinger", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/41", abstract = "Genetic models incorporating resampling and migration are now fairly well-understood. Problems arise in the analysis, if both selection and mutation are incorporated. This paper addresses some aspects of this problem, in particular the analysis of the long-time behaviour before the equilibrium is reached (quasi-equilibrium, which is the time range of interest in most applications).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Interacting Fleming--Viot processes, Renormalization analysis, Selection, Mutation, Recombination", } @Article{Dohmen:1999:IIE, author = "Klaus Dohmen", title = "Improved Inclusion--Exclusion Identities and Inequalities Based on a Particular Class of Abstract Tubes", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "5:1--5:12", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-42", ISSN = "1083-6489", MRclass = "05A15 (05A19 05A20 68M15 90B25)", MRnumber = "1684161 (2000a:05009)", MRreviewer = "Stephen Tanny", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/42", abstract = "Recently, Naiman and Wynn introduced the concept of an abstract tube in order to obtain improved inclusion-exclusion identities and inequalities that involve much fewer terms than their classical counterparts. In this paper, we introduce a particular class of abstract tubes which plays an important role with respect to chromatic polynomials and network reliability. The inclusion-exclusion identities and inequalities associated with this class simultaneously generalize several well-known results such as Whitney's broken circuit theorem, Shier's expression for the reliability of a network as an alternating sum over chains in a semilattice and Narushima's inclusion-exclusion identity for posets. Moreover, we show that under some restrictive assumptions a polynomial time inclusion-exclusion algorithm can be devised, which generalizes an important result of Provan and Ball on network reliability.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Inclusion-exclusion, Bonferroni inequalities, sieve formula, abstract tube, abstract simplicial complex, partial order, chain, dynamic programming, graph coloring, chromatic polynomial, broken circuit complex, network reliability", } @Article{Dalang:1999:EMM, author = "Robert C. Dalang", title = "Extending the Martingale Measure Stochastic Integral With Applications to Spatially Homogeneous S.P.D.E.'s", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "6:1--6:29", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-43", ISSN = "1083-6489", MRclass = "60H05 (35R60 60G15 60G48 60H15)", MRnumber = "1684157 (2000b:60132)", MRreviewer = "Marta Sanz Sol{\'e}", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/43", abstract = "We extend the definition of Walsh's martingale measure stochastic integral so as to be able to solve stochastic partial differential equations whose Green's function is not a function but a Schwartz distribution. This is the case for the wave equation in dimensions greater than two. Even when the integrand is a distribution, the value of our stochastic integral process is a real-valued martingale. We use this extended integral to recover necessary and sufficient conditions under which the linear wave equation driven by spatially homogeneous Gaussian noise has a process solution, and this in any spatial dimension. Under this condition, the non-linear three dimensional wave equation has a global solution. The same methods apply to the damped wave equation, to the heat equation and to various parabolic equations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic wave equation, stochastic heat equation, Gaussian noise, process solution", } @Article{Arcones:1999:WCR, author = "Miguel A. Arcones", title = "Weak Convergence for the Row Sums of a Triangular Array of Empirical Processes Indexed by a Manageable Triangular Array of Functions", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "7:1--7:17", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-44", ISSN = "1083-6489", MRclass = "60B12 (60F17)", MRnumber = "1684153 (2000c:60004)", MRreviewer = "Lajos Horv{\'a}th", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/44", abstract = "We study the weak convergence for the row sums of a general triangular array of empirical processes indexed by a manageable class of functions converging to an arbitrary limit. As particular cases, we consider random series processes and normalized sums of i.i.d. random processes with Gaussian and stable limits. An application to linear regression is presented. In this application, the limit of the row sum of a triangular array of empirical process is the mixture of a Gaussian process with a random series process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Empirical processes, triangular arrays, manageable classes", } @Article{Worms:1999:MDS, author = "Julien Worms", title = "Moderate deviations for stable {Markov} chains and regression models", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "8:1--8:28", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-45", ISSN = "1083-6489", MRclass = "60F10 (60G10 62J02 62J05)", MRnumber = "1684149 (2000b:60073)", MRreviewer = "Peter Eichelsbacher", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/45", abstract = "We prove moderate deviations principles for \begin{itemize} \item unbounded additive functionals of the form $ S_n = \sum_{j = 1}^n g(X^{(p)}_{j - 1}) $, where $ (X_n)_{n \in N} $ is a stable $ R^d$-valued functional autoregressive model of order $p$ with white noise and stationary distribution $ \mu $, and $g$ is an $ R^q$-valued Lipschitz function of order $ (r, s)$; \item the error of the least squares estimator (LSE) of the matrix $ \theta $ in an $ R^d$-valued regression model $ X_n = \theta^t \phi_{n - 1} + \epsilon_n$, where $ (\epsilon_n)$ is a generalized Gaussian noise. \end{itemize} We apply these results to study the error of the LSE for a stable $ R^d$-valued linear autoregressive model of order $p$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Large and Moderate Deviations, Martingales, Markov Chains, Least Squares Estimator for a regression model", } @Article{Morters:1999:SSL, author = "Peter M{\"o}rters and Narn-Rueih Shieh", title = "Small scale limit theorems for the intersection local times of {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "9:1--9:23", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-46", ISSN = "1083-6489", MRclass = "60G17 (28A78 60J55 60J65)", MRnumber = "1690313 (2000e:60060)", MRreviewer = "Yimin Xiao", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/46", abstract = "In this paper we contribute to the investigation of the fractal nature of the intersection local time measure on the intersection of independent Brownian paths. We particularly point out the difference in the small scale behaviour of the intersection local times in three-dimensional space and in the plane by studying almost sure limit theorems motivated by the notion of average densities introduced by Bedford and Fisher. We show that in 3-space the intersection local time measure of two paths has an average density of order two with respect to the gauge function $ \varphi (r) = r $, but in the plane, for the intersection local time measure of p Brownian paths, the average density of order two fails to converge. The average density of order three, however, exists for the gauge function $ \varphi_p(r) = r^2 [\log (1 / r)]^p $. We also prove refined versions of the above results, which describe more precisely the fluctuations of the volume of small balls around these gauge functions by identifying the density distributions, or lacunarity distributions, of the intersection local times.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, intersection local time, Palm distribution, average density, density distribution, lacunarity distribution, logarithmic average", } @Article{Dembo:1999:TPT, author = "Amir Dembo and Yuval Peres and Jay Rosen and Ofer Zeitouni", title = "Thick Points for Transient Symmetric Stable Processes", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "10:1--10:13", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-47", ISSN = "1083-6489", MRclass = "60J55 (60G52)", MRnumber = "1690314 (2000f:60117)", MRreviewer = "Larbi Alili", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/47", abstract = "Let $ T(x, r) $ denote the total occupation measure of the ball of radius $r$ centered at $x$ for a transient symmetric stable processes of index $ b < d$ in $ R^d$ and $ K(b, d)$ denote the norm of the convolution with its 0-potential density, considered as an operator on $ L^2 (B(0, 1), d x)$. We prove that as $r$ approaches 0, almost surely $ \sup_{|x| \leq 1} T(x, r) / (r^b| \log r|) \to b K(b, d)$. Furthermore, for any $ a \in (0, b / K(b, d))$, the Hausdorff dimension of the set of ``thick points'' $x$ for which $ \limsup_{r \to 0} T(x, r) / (r^b | \log r|) = a$, is almost surely $ b - a / K(b, d)$; this is the correct scaling to obtain a nondegenerate ``multifractal spectrum'' for transient stable occupation measure. The liminf scaling of $ T(x, r)$ is quite different: we exhibit positive, finite, non-random $ c(b, d), C(b, d)$, such that almost surely $ c(b, d) < \sup_x \liminf_{r \to 0} T(x, r) / r^b < C(b, d)$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stable process, occupation measure, multifractal spectrum", } @Article{Pitman:1999:BMB, author = "Jim Pitman", title = "{Brownian} motion, bridge, excursion, and meander characterized by sampling at independent uniform times", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "11:1--11:33", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-48", ISSN = "1083-6489", MRclass = "60J65 (05A19 11B73)", MRnumber = "1690315 (2000e:60137)", MRreviewer = "G{\"o}tz Kersting", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/48; http://www.math.washington.edu/~ejpecp/EjpVol4/paper11.abs.html", abstract = "For a random process $X$ consider the random vector defined by the values of $X$ at times $ 0 < U_{n, 1} < \cdots {} < U_{n, n} < 1$ and the minimal values of $X$ on each of the intervals between consecutive pairs of these times, where the $ U_{n, i}$ are the order statistics of $n$ independent uniform $ (0, 1)$ variables, independent of $X$. The joint law of this random vector is explicitly described when $X$ is a Brownian motion. Corresponding results for Brownian bridge, excursion, and meander are deduced by appropriate conditioning. These descriptions yield numerous new identities involving the laws of these processes, and simplified proofs of various known results, including Aldous's characterization of the random tree constructed by sampling the excursion at $n$ independent uniform times, Vervaat's transformation of Brownian bridge into Brownian excursion, and Denisov's decomposition of the Brownian motion at the time of its minimum into two independent Brownian meanders. Other consequences of the sampling formulae are Brownian representations of various special functions, including Bessel polynomials, some hypergeometric polynomials, and the Hermite function. Various combinatorial identities involving random partitions and generalized Stirling numbers are also obtained.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "alternating exponential random walk, uniform order statistics, critical binary random tree, Vervaat's transformation, random partitions, generalized Stirling numbers, Bessel polynomials, McDonald function, products of gamma variables, Hermite function", } @Article{Greven:1999:LBB, author = "Andreas Greven and Achim Klenke and Anton Wakolbinger", title = "The Longtime Behavior of Branching Random Walk in a Catalytic Medium", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "12:1--12:80", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-49", ISSN = "1083-6489", MRclass = "60K35 (60J80)", MRnumber = "1690316 (2000a:60189)", MRreviewer = "T. M. Liggett", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/49", abstract = "Consider a countable collection of particles located on a countable group, performing a critical branching random walk where the branching rate of a particle is given by a random medium fluctuating both in space and time. Here we study the case where the time-space random medium (called catalyst) is also a critical branching random walk evolving autonomously while the local branching rate of the reactant process is proportional to the number of catalytic particles present at a site. The catalyst process and the reactant process typically have different underlying motions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching random walk in random medium, reactant-catalyst systems, interacting particle Systems, random media", } @Article{Peligrad:1999:CSS, author = "Magda Peligrad", title = "Convergence of Stopped Sums of Weakly Dependent Random Variables", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "13:1--13:13", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-50", ISSN = "1083-6489", MRclass = "60E15 (60F15 60G48)", MRnumber = "1692676 (2000d:60033)", MRreviewer = "Przemys{\l}aw Matu{\l}a", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/50", abstract = "In this paper we investigate stopped partial sums for weak dependent sequences.\par In particular, the results are used to obtain new maximal inequalities for strongly mixing sequences and related almost sure results.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Partial sums, maximal inequalities, weak dependent sequences, stopping times, amarts", } @Article{Steinsaltz:1999:RTC, author = "David Steinsaltz", title = "Random Time Changes for Sock-Sorting and Other Stochastic Process Limit Theorems", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "14:1--14:25", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-51", ISSN = "1083-6489", MRclass = "60F05 (60C05 60K05)", MRnumber = "1692672 (2000e:60038)", MRreviewer = "Lars Holst", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/51", abstract = "A common technique in the theory of stochastic process is to replace a discrete time coordinate by a continuous randomized time, defined by an independent Poisson or other process. Once the analysis is complete on this Poissonized process, translating the results back to the original setting may be nontrivial. It is shown here that, under fairly general conditions, if the process $ S_n $ and the time change $ \phi_n $ both converge, when normalized by the same constant, to limit processes combined process $ S_n(\phi_n(t)) $ converges, when properly normalized, to a sum of the limit of the original process, and the limit of the time change multiplied by the derivative of $ E S_n $. It is also shown that earlier results on the fine structure of the maxima are preserved by these time changes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "maximal inequalities, decoupling, Poissonization, functional central limit theorem, sorting, random allocations, auxiliary randomization, time change", } @Article{Pitman:1999:LMB, author = "Jim Pitman and Marc Yor", title = "The law of the maximum of a {Bessel} bridge", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "15:1--15:35", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-52", ISSN = "1083-6489", MRclass = "60J65 (33C10 60J60)", MRnumber = "1701890 (2000j:60101)", MRreviewer = "Endre Cs{\'a}ki", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/52; http://www.math.washington.edu/~ejpecp/EjpVol4/paper15.abs.html", abstract = "Let $ M_d $ be the maximum of a standard Bessel bridge of dimension $d$. A series formula for $ P(M_d \leq a)$ due to Gikhman and Kiefer for $ d = 1, 2, \ldots $ is shown to be valid for all real $ d > 0$. Various other characterizations of the distribution of $ M_d$ are given, including formulae for its Mellin transform, which is an entire function. The asymptotic distribution of $ M_d$ is described both as $d$ tends to infinity and as $d$ tends to zero.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian bridge, Brownian excursion, Brownian scaling, local time, Bessel process, zeros of Bessel functions, Riemann zeta function", } @Article{Igloi:1999:LRD, author = "E. Igl{\'o}i and G. Terdik", title = "Long-range dependence through gamma-mixed {Ornstein--Uhlenbeck} process", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "16:1--16:33", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-53", ISSN = "1083-6489", MRclass = "60H05 (60G15 60G18 60H10)", MRnumber = "1713649 (2000m:60060)", MRreviewer = "V. V. Anh", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/53", abstract = "The limit process of aggregational models---(i) sum of random coefficient AR(1) processes with independent Brownian motion (BM) inputs and (ii) sum of AR(1) processes with random coefficients of Gamma distribution and with input of common BM's, ---proves to be Gaussian and stationary and its transfer function is the mixture of transfer functions of Ornstein--Uhlenbeck (OU) processes by Gamma distribution. It is called Gamma-mixed Ornstein--Uhlenbeck process ($ \Gamma \mathsf {MOU}$). For independent Poisson alternating $0$-$1$ reward processes with proper random intensity it is shown that the standardized sum of the processes converges to the standardized $ \Gamma \mathsf {MOU}$ process. The $ \Gamma \mathsf {MOU}$ process has various interesting properties and it is a new candidate for the successful modelling of several Gaussian stationary data with long-range dependence. Possible applications and problems are also considered.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stationarity, Long-range dependence, Spectral representation, Ornstein--Uhlenbeck process, Aggregational model, Stochastic differentialequation, Fractional Brownian motion input, Heart rate variability", } @Article{Liptser:1999:MDT, author = "R. Liptser and V. Spokoiny", title = "Moderate Deviations Type Evaluation for Integral Functionals of Diffusion Processes", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "17:1--17:25", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-54", ISSN = "1083-6489", MRclass = "60F10 (60J60)", MRnumber = "1741723 (2001j:60054)", MRreviewer = "Anatolii A. Pukhal{\cprime}ski{\u\i}", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/54", abstract = "We establish a large deviations type evaluation for the family of integral functionals.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "large deviations, moderate deviations, diffusion", } @Article{Fukushima:1999:SMC, author = "Masatoshi Fukushima", title = "On semi-martingale characterizations of functionals of symmetric {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "18:1--18:32", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-55", ISSN = "1083-6489", MRclass = "60J45 (31C25 60J55)", MRnumber = "1741537 (2001b:60091)", MRreviewer = "Zhen-Qing Chen", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/55", abstract = "For a quasi-regular (symmetric) Dirichlet space $ ({\cal E}, {\cal F}) $ and an associated symmetric standard process $ (X_t, P_x) $, we show that, for $ u i n {\cal F} $, the additive functional $ u^*(X_t) - u^*(X_0) $ is a semimartingale if and only if there exists an $ {\cal E}$-nest $ \{ F_n \} $ and positive constants $ C_n$ such that $ \vert {\cal E}(u, v) \vert \leq C_n \Vert v \Vert_\infty, v \in {\cal F}_{F_n, b}.$ In particular, a signed measure resulting from the inequality will be automatically smooth. One of the variants of this assertion is applied to the distorted Brownian motion on a closed subset of $ R^d$, giving stochastic characterizations of BV functions and Caccioppoli sets.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "quasi-regular Dirichlet form, strongly regular representation, additive functionals, semimartingale, smooth signed measure, BV function", } @Article{Getoor:1999:EGS, author = "Ronald K. Getoor", title = "An Extended Generator and {Schr{\"o}dinger} Equations", journal = j-ELECTRON-J-PROBAB, volume = "4", pages = "19:1--19:23", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v4-56", ISSN = "1083-6489", MRclass = "60J40 (60J25 60J35 60J45)", MRnumber = "1741538 (2001c:60115)", MRreviewer = "Zoran Vondra{\v{c}}ek", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/56", abstract = "The generator of a Borel right process is extended so that it maps functions to smooth measures. This extension may be defined either probabilistically using martingales or analytically in terms of certain kernels on the state space of the process. Then the associated Schr{\"o}dinger equation with a (signed) measure serving as potential may be interpreted as an equation between measures. In this context general existence and uniqueness theorems for solutions are established. These are then specialized to obtain more concrete results in special situations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov processes, Schr{\"o}dinger equations, generators, smooth measures", } @Article{Sharpe:1999:MRS, author = "Michael Sharpe", title = "Martingales on Random Sets and the Strong Martingale Property", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "1:1--1:17", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-57", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/57", abstract = "Let $X$ be a process defined on an optional random set. The paper develops two different conditions on $X$ guaranteeing that it is the restriction of a uniformly integrable martingale. In each case, it is supposed that $X$ is the restriction of some special semimartingale $Z$ with canonical decomposition $ Z = M + A$. The first condition, which is both necessary and sufficient, is an absolute continuity condition on $A$. Under additional hypotheses, the existence of a martingale extension can be characterized by a strong martingale property of $X$. Uniqueness of the extension is also considered.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Martingale, random set, strong martingale property", } @Article{Camarri:1999:LDR, author = "Michael Camarri and Jim Pitman", title = "Limit Distributions and Random Trees Derived from the Birthday Problem with Unequal Probabilities", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "2:1--2:18", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-58", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/58", abstract = "Given an arbitrary distribution on a countable set, consider the number of independent samples required until the first repeated value is seen. Exact and asymptotic formulae are derived for the distribution of this time and of the times until subsequent repeats. Asymptotic properties of the repeat times are derived by embedding in a Poisson process. In particular, necessary and sufficient conditions for convergence are given and the possible limits explicitly described. Under the same conditions the finite dimensional distributions of the repeat times converge to the arrival times of suitably modified Poisson processes, and random trees derived from the sequence of independent trials converge in distribution to an inhomogeneous continuum random tree.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Repeat times, point process, Poisson embedding, inhomogeneous continuum random tree, Rayleigh distribution", } @Article{Bessaih:1999:SWA, author = "Hakima Bessaih", title = "Stochastic Weak Attractor for a Dissipative {Euler} Equation", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "3:1--3:16", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-59", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/59", abstract = "In this paper a nonautonomous dynamical system is considered, a stochastic one that is obtained from the dissipative Euler equation subject to a stochastic perturbation, an additive noise. Absorbing sets have been defined as sets that depend on time and attracts from $ - \infty $. A stochastic weak attractor is constructed in phase space with respect to two metrics and is compact in the lower one.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dissipative Euler Equation, random dynamical systems, attractors", } @Article{Bertoin:1999:TCD, author = "Jean Bertoin and Jim Pitman", title = "Two Coalescents Derived from the Ranges of Stable Subordinators", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "7:1--7:17", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-63", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/63", abstract = "Let $ M_\alpha $ be the closure of the range of a stable subordinator of index $ \alpha \in]0, 1 [ $. There are two natural constructions of the $ M_{\alpha } $'s simultaneously for all $ \alpha \in]0, 1 [ $, so that $ M_{\alpha } \subseteq M_{\beta } $ for $ 0 < \alpha < \beta < 1 $: one based on the intersection of independent regenerative sets and one based on Bochner's subordination. We compare the corresponding two coalescent processes defined by the lengths of complementary intervals of $ [0, 1] \backslash M_{1 - \rho } $ for $ 0 < \rho < 1 $. In particular, we identify the coalescent based on the subordination scheme with the coalescent recently introduced by Bolthausen and Sznitman.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coalescent, stable, subordinator, Poisson--Dirichlet distribution", } @Article{Khoshnevisan:2000:LRF, author = "Davar Khoshnevisan and Yuval Peres and Yimin Xiao", title = "Limsup Random Fractals", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "4:1--4:24", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-60", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/60", abstract = "Orey and Taylor (1974) introduced sets of ``fast points'' where Brownian increments are exceptionally large, $ {\rm F}(\lambda) := \{ t \in [0, 1] \colon \limsup_{h \to 0}{ | X(t + h) - X(t)| / \sqrt { 2h| \log h|}} \ge \lambda \} $. They proved that for $ \lambda \in (0, 1] $, the Hausdorff dimension of $ {\rm F}(\lambda) $ is $ 1 - \lambda^2 $ a.s. We prove that for any analytic set $ E \subset [0, 1] $, the supremum of the $ \lambda $ such that $E$ intersects $ {\rm F}(\lambda)$ a.s. equals $ \sqrt {\text {dim}_p E }$, where $ \text {dim}_p E$ is the {\em packing dimension} of $E$. We derive this from a general result that applies to many other random fractals defined by limsup operations. This result also yields extensions of certain ``fractal functional limit laws'' due to Deheuvels and Mason (1994). In particular, we prove that for any absolutely continuous function $f$ such that $ f(0) = 0$ and the energy $ \int_0^1 |f'|^2 \, d t $ is lower than the packing dimension of $E$, there a.s. exists some $ t \in E$ so that $f$ can be uniformly approximated in $ [0, 1]$ by normalized Brownian increments $ s \mapsto [X(t + s h) - X(t)] / \sqrt { 2h| \log h|}$; such uniform approximation is a.s. impossible if the energy of $f$ is higher than the packing dimension of $E$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Limsup random fractal, packing dimension, Hausdorff dimension, Brownian motion, fast point", } @Article{Ichinose:2000:NED, author = "Takashi Ichinose and Satoshi Takanobu", title = "The Norm Estimate of the Difference Between the {Kac} Operator and {Schr{\"o}dinger} Semigroup {II}: The General Case Including the Relativistic Case", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "5:1--5:47", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-61", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/61", abstract = "More thorough results than in our previous paper in Nagoya Math. J. are given on the $ L_p$-operator norm estimates for the Kac operator $ e^{-tV / 2} e^{-tH_0} e^{-tV / 2}$ compared with the Schr{\"o}dinger semigroup $ e^{-t(H_0 + V)}$. The Schr{\"o}dinger operators $ H_0 + V$ to be treated in this paper are more general ones associated with the L{\'e}vy process, including the relativistic Schr{\"o}dinger operator. The method of proof is probabilistic based on the Feynman--Kac formula. It differs from our previous work in the point of using {\em the Feynman--Kac formula\/} not directly for these operators, but instead through {\em subordination\/} from the Brownian motion, which enables us to deal with all these operators in a unified way. As an application of such estimates the Trotter product formula in the $ L_p$-operator norm, with error bounds, for these Schr{\"o}dinger semigroups is also derived.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Schr{\"o}dinger operator, Schr{\"o}dinger semigroup, relativistic Schr{\"o}dinger operator, Trotter product formula, Lie--Trotter--Kato product formula, Feynman--Kac formula, subordination of Brownian motion, Kato's inequality", } @Article{Mikulevicius:2000:SEE, author = "R. Mikulevicius and G. Valiukevicius", title = "On Stochastic {Euler} equation in $ \mathbb {R}^d $", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "6:1--6:20", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-62", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/62", abstract = "Following the Arnold--Marsden--Ebin approach, we prove local (global in 2-D) existence and uniqueness of classical (H{\"o}lder class) solutions of stochastic Euler equation with random forcing.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic partial differential equations, Euler equation", } @Article{Lawler:2000:SCH, author = "Gregory Lawler", title = "Strict Concavity of the Half Plane Intersection Exponent for Planar {Brownian} Motion", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "8:1--8:33", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-64", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/64", abstract = "The intersection exponents for planar Brownian motion measure the exponential decay of probabilities of nonintersection of paths. We study the intersection exponent $ \xi (\lambda_1, \lambda_2) $ for Brownian motion restricted to a half plane which by conformal invariance is the same as Brownian motion restricted to an infinite strip. We show that $ \xi $ is a strictly concave function. This result is used in another paper to establish a universality result for conformally invariant intersection exponents.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, intersection exponent", } @Article{Conlon:2000:HEE, author = "Joseph Conlon and Ali Naddaf", title = "On Homogenization Of Elliptic Equations With Random Coefficients", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "9:1--9:58", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-65", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/65", abstract = "In this paper, we investigate the rate of convergence of the solution $ u_\varepsilon $ of the random elliptic partial difference equation $ (\nabla^{\varepsilon *} a(x / \varepsilon, \omega) \nabla^\varepsilon + 1)u_\varepsilon (x, \omega) = f(x) $ to the corresponding homogenized solution. Here $ x \in \varepsilon Z^d $, and $ \omega \in \Omega $ represents the randomness. Assuming that $ a(x) $'s are independent and uniformly elliptic, we shall obtain an upper bound $ \varepsilon^\alpha $ for the rate of convergence, where $ \alpha $ is a constant which depends on the dimension $ d \ge 2 $ and the deviation of $ a(x, \omega) $ from the identity matrix. We will also show that the (statistical) average of $ u_\varepsilon (x, \omega) $ and its derivatives decay exponentially for large $x$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Homogenization, elliptic equations, random environment, Euler-Lagrange equation", } @Article{Hu:2000:LCH, author = "Yueyun Hu", title = "The Laws of {Chung} and {Hirsch} for {Cauchy}'s Principal Values Related to {Brownian} Local Times", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "10:1--10:16", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-66", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/66", abstract = "Two Chung-type and Hirsch-type laws are established to describe the liminf asymptotic behaviours of the Cauchy's principal values related to Brownian local times. These results are generalized to a class of Brownian additive functionals.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Principal values, Brownian additive functional, liminf asymptotic behaviours", } @Article{Feyel:2000:ARP, author = "D. Feyel and A. {de La Pradelle}", title = "The Abstract {Riemannian} Path Space", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "11:1--11:17", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-67", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/67", abstract = "On the Wiener space $ \Omega $, we introduce an abstract Ricci process $ A_t $ and a pseudo-gradient $ F \rightarrow {F}^\sharp $ which are compatible through an integration by parts formula. They give rise to a $ \sharp $-Sobolev space on $ \Omega $, logarithmic Sobolev inequalities, and capacities, which are tight on Hoelder compact sets of $ \Omega $. These are then applied to the path space over a Riemannian manifold.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Wiener space, Sobolev spaces, Bismut--Driver formula, Logarithmic Sobolev inequality, Capacities, Riemannian manifold path space", } @Article{Schweinsberg:2000:CSM, author = "Jason Schweinsberg", title = "Coalescents with Simultaneous Multiple Collisions", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "12:1--12:50", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-68", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/68", abstract = "We study a family of coalescent processes that undergo ``simultaneous multiple collisions, '' meaning that many clusters of particles can merge into a single cluster at one time, and many such mergers can occur simultaneously. This family of processes, which we obtain from simple assumptions about the rates of different types of mergers, essentially coincides with a family of processes that Mohle and Sagitov obtain as a limit of scaled ancestral processes in a population model with exchangeable family sizes. We characterize the possible merger rates in terms of a single measure, show how these coalescents can be constructed from a Poisson process, and discuss some basic properties of these processes. This work generalizes some work of Pitman, who provides similar analysis for a family of coalescent processes in which many clusters can coalesce into a single cluster, but almost surely no two such mergers occur simultaneously.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coalescence, ancestral processes, Poisson point processes, Markov processes, exchangeable random partitions", } @Article{Krylov:2000:SS, author = "N. Krylov", title = "{SPDEs} in {$ L_q((0, \tau], L_p) $} Spaces", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "13:1--13:29", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-69", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/69", abstract = "Existence and uniqueness theorems are presented for evolutional stochastic partial differential equations of second order in $ L_p$-spaces with weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to space and time variables to be different.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic partial differential equations, Sobolev spaces with weights", } @Article{Lyne:2000:TWC, author = "Owen Lyne", title = "Travelling Waves for a Certain First-Order Coupled {PDE} System", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "14:1--14:40", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-70", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/70", abstract = "This paper concentrates on a particular first-order coupled PDE system. It provides both a detailed treatment of the {\em existence\/} and {\em uniqueness\/} of monotone travelling waves to various equilibria, by differential-equation theory and by probability theory and a treatment of the corresponding hyperbolic initial-value problem, by analytic methods. The initial-value problem is studied using characteristics to show existence and uniqueness of a bounded solution for bounded initial data (subject to certain smoothness conditions). The concept of {\em weak\/} solutions to partial differential equations is used to rigorously examine bounded initial data with jump discontinuities. For the travelling wave problem the differential-equation treatment makes use of a shooting argument and explicit calculations of the eigenvectors of stability matrices. The probabilistic treatment is careful in its proofs of {\em martingale\/} (as opposed to merely local-martingale) properties. A modern {\em change-of-measure technique\/} is used to obtain the best lower bound on the speed of the monotone travelling wave --- with Heaviside initial conditions the solution converges to an approximate travelling wave of that speed (the solution tends to one ahead of the wave-front and to zero behind it). Waves to different equilibria are shown to be related by Doob $h$-transforms. {\em Large-deviation theory\/} provides heuristic links between alternative descriptions of minimum wave speeds, rigorous algebraic proofs of which are provided.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Travelling waves, Martingales, Branching processes", } @Article{Kopp:2000:CIM, author = "P. Kopp and Volker Wellmann", title = "Convergence in Incomplete Market Models", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "15:1--15:26", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-71", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/71", abstract = "The problem of pricing and hedging of contingent claims in incomplete markets has led to the development of various valuation methodologies. This paper examines the mean-variance approach to risk-minimisation and shows that it is robust under the convergence from discrete- to continuous-time market models. This property yields new convergence results for option prices, trading strategies and value processes in incomplete market models. Techniques from nonstandard analysis are used to develop new results for the lifting property of the minimal martingale density and risk-minimising strategies. These are applied to a number of incomplete market models:\par It is shown that the convergence of the underlying models implies the convergence of strategies and value processes for multinomial models and approximations of the Black--Scholes model by direct discretisation of the price process. The concept of $ D^2$-convergence is extended to these classes of models, including the construction of discretisation schemes. This yields new standard convergence results for these models.\par For ease of reference a summary of the main results from nonstandard analysis in the context of stochastic analysis is given as well as a brief introduction to mean-variance hedging and pricing.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Financial models, incomplete markets", } @Article{Goldsheid:2000:ECA, author = "Ilya Goldsheid and Boris Khoruzhenko", title = "Eigenvalue Curves of Asymmetric Tridiagonal Matrices", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "16:1--16:28", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-72", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/72", abstract = "Random Schr{\"o}dinger operators with imaginary vector potentials are studied in dimension one. These operators are non-Hermitian and their spectra lie in the complex plane. We consider the eigenvalue problem on finite intervals of length $n$ with periodic boundary conditions and describe the limit eigenvalue distribution when $n$ goes to infinity. We prove that this limit distribution is supported by curves in the complex plane. We also obtain equations for these curves and for the corresponding eigenvalue density in terms of the Lyapunov exponent and the integrated density of states of a ``reference'' symmetric eigenvalue problem. In contrast to these results, the spectrum of the limit operator in $ \ell^2 (Z)$ is a two dimensional set which is not approximated by the spectra of the finite-interval operators.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random matrix, Schr{\"o}dinger operator, Lyapunov exponent, eigenvalue distribution, complex eigenvalue.", } @Article{Geiger:2000:PPP, author = "Jochen Geiger", title = "{Poisson} point process limits in size-biased {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "5", pages = "17:1--17:12", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v5-73", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/73", abstract = "Consider a critical binary continuous-time Galton--Watson tree size-biased according to the number of particles at time $t$. Decompose the population at $t$ according to the particles' degree of relationship with a distinguished particle picked purely at random from those alive at $t$. Keeping track of the times when the different families grow out of the distinguished line of descent and the related family sizes at $t$, we represent this relationship structure as a point process in a time-size plane. We study limits of these point processes in the single- and some multitype case.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Galton--Watson process, random tree, point process, limit laws", } @Article{Sengupta:2000:FPD, author = "Arindam Sengupta and Anish Sarkar", title = "Finitely Polynomially Determined {L{\'e}vy} Processes", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "7:1--7:22", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-80", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/80", abstract = "A time-space harmonic polynomial for a continuous-time process $ X = \{ X_t \colon t \ge 0 \} $ is a two-variable polynomial $P$ such that $ \{ P(t, X_t) \colon t \ge 0 \} $ is a martingale for the natural filtration of $X$. Motivated by L{\'e}vy's characterisation of Brownian motion and Watanabe's characterisation of the Poisson process, we look for classes of processes with reasonably general path properties in which a characterisation of those members whose laws are determined by a finite number of such polynomials is available. We exhibit two classes of processes, the first containing the L{\'e}vy processes, and the second a more general class of additive processes, with this property and describe the respective characterisations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "L{\'e}vy process, additive process, L{\'e}vy's characterisation, L{\'e}vy measure, Kolmogorov measure", } @Article{Mountford:2001:NLB, author = "Thomas Mountford", title = "A Note on Limiting Behaviour of Disastrous Environment Exponents", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "1:1--1:10", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-74", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/74", abstract = "We consider a random walk on the $d$-dimensional lattice and investigate the asymptotic probability of the walk avoiding a ``disaster'' (points put down according to a regular Poisson process on space-time). We show that, given the Poisson process points, almost surely, the chance of surviving to time $t$ is like $ e^{- \alpha \log (\frac 1k) t } $, as $t$ tends to infinity if $k$, the jump rate of the random walk, is small.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walk, disaster point, Poisson process", } @Article{Su:2001:DCD, author = "Francis Su", title = "Discrepancy Convergence for the Drunkard's Walk on the Sphere", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "2:1--2:20", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-75", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/75", abstract = "We analyze the drunkard's walk on the unit sphere with step size $ \theta $ and show that the walk converges in order $ C / \sin^2 (\theta) $ steps in the discrepancy metric ($C$ a constant). This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "discrepancy, random walk, Gelfand pairs, homogeneous spaces, Legendre polynomials", } @Article{Bai:2001:LTN, author = "Zhi-Dong Bai and Hsien-Kuei Hwang and Wen-Qi Liang and Tsung-Hsi Tsai", title = "Limit Theorems for the Number of Maxima in Random Samples from Planar Regions", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "3:1--3:41", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-76", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/76", abstract = "We prove that the number of maximal points in a random sample taken uniformly and independently from a convex polygon is asymptotically normal in the sense of convergence in distribution. Many new results for other planar regions are also derived. In particular, precise Poisson approximation results are given for the number of maxima in regions bounded above by a nondecreasing curve.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Maximal points, multicriterial optimization, central limit theorems, Poisson approximations, convex polygons", } @Article{Kesten:2001:PAW, author = "Harry Kesten and Vladas Sidoravicius and Yu Zhang", title = "Percolation of Arbitrary words on the Close-Packed Graph of $ \mathbb {Z}^2 $", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "4:1--4:27", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-77", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/77", abstract = "Let $ {\mathbb {Z}}^2_{cp} $ be the close-packed graph of $ \mathbb {Z}^2 $, that is, the graph obtained by adding to each face of $ \mathbb {Z}^2 $ its diagonal edges. We consider site percolation on $ \mathbb {Z}^2_{cp} $, namely, for each $v$ we choose $ X(v) = 1$ or 0 with probability $p$ or $ 1 - p$, respectively, independently for all vertices $v$ of $ \mathbb {Z}^2_{cp}$. We say that a word $ (\xi_1, \xi_2, \dots) \in \{ 0, 1 \}^{\mathbb {N}}$ is seen in the percolation configuration if there exists a selfavoiding path $ (v_1, v_2, \dots)$ on $ \mathbb {Z}^2_{cp}$ with $ X(v_i) = \xi_i, i \ge 1$. $ p_c(\mathbb {Z}^2, \text {site})$ denotes the critical probability for site-percolation on $ \mathbb {Z}^2$. We prove that for each fixed $ p \in \big (1 - p_c(\mathbb {Z}^2, \text {site}), p_c(\mathbb {Z}^2, \text {site}) \big)$, with probability 1 all words are seen. We also show that for some constants $ C_i > 0$ there is a probability of at least $ C_1$ that all words of length $ C_0 n^2$ are seen along a path which starts at a neighbor of the origin and is contained in the square $ [ - n, n]^2$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Percolation, close-packing", } @Article{Flandoli:2001:SSS, author = "Franco Flandoli and Marco Romito", title = "Statistically Stationary Solutions to the {$3$D} {Navier--Stokes} Equations do not show Singularities", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "5:1--5:15", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-78", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/78", abstract = "If $ \mu $ is a probability measure on the set of suitable weak solutions of the 3D Navier--Stokes equations, invariant for the time-shift, with finite mean dissipation rate, then at every time $t$ the set of singular points is empty $ \mu $-a.s. The existence of a measure $ \mu $ with the previous properties is also proved; it may describe a turbulent asymptotic regime.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Navier--Stokes equations, suitable weak solutions, stationary solutions", } @Article{DeSantis:2001:SIP, author = "Emilio {De Santis}", title = "Strict Inequality for Phase Transition between Ferromagnetic and Frustrated Systems", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "6:1--6:27", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-79", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/79", abstract = "We consider deterministic and disordered frustrated systems in which we can show some strict inequalities with respect to related ferromagnetic systems. A case particularly interesting is the Edwards--Anderson spin-glass model in which it is possible to determine a region of uniqueness of the Gibbs measure, which is strictly larger than the region of uniqueness for the related ferromagnetic system. We analyze also deterministic systems with $ |J_b| \in [J_A, J_B] $ where $ 0 < J_A \leq J_B < \infty $, for which we prove strict inequality for the critical points of the related FK model. The results are obtained for the Ising models but some extensions to Potts models are possible.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Phase transition, Ising model, disordered systems, stochastic order", } @Article{Heck:2001:PLD, author = "Matthias Heck and Fa{\"\i}za Maaouia", title = "The Principle of Large Deviations for Martingale Additive Functionals of Recurrent {Markov} Processes", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "8:1--8:26", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-81", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/81", abstract = "We give a principle of large deviations for a generalized version of the strong central limit theorem. This generalized version deals with martingale additive functionals of a recurrent Markov process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central Limit Theorem (CLT), Large Deviations Principle (LDP), Markov Processes, Autoregressive Model (AR1), Positive Recurrent Processes, Martingale Additive Functional (MAF)", } @Article{Barlow:2001:TDA, author = "Martin Barlow and Takashi Kumagai", title = "Transition Density Asymptotics for Some Diffusion Processes with Multi-Fractal Structures", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "9:1--9:23", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-82", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/82", abstract = "We study the asymptotics as $ t \to 0 $ of the transition density of a class of $ \mu $-symmetric diffusions in the case when the measure $ \mu $ has a multi-fractal structure. These diffusions include singular time changes of Brownian motion on the unit cube.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Diffusion process, heat equation, transition density, spectral dimension, multi-fractal", } @Article{Pemantle:2001:WDB, author = "Robin Pemantle and Yuval Peres and Jim Pitman and Marc Yor", title = "Where Did the {Brownian} Particle Go?", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "10:1--10:22", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-83", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/83", abstract = "Consider the radial projection onto the unit sphere of the path a $d$-dimensional Brownian motion $W$, started at the center of the sphere and run for unit time. Given the occupation measure $ \mu $ of this projected path, what can be said about the terminal point $ W(1)$, or about the range of the original path? In any dimension, for each Borel set $A$ in $ S^{d - 1}$, the conditional probability that the projection of $ W(1)$ is in $A$ given $ \mu (A)$ is just $ \mu (A)$. Nevertheless, in dimension $ d \ge 3$, both the range and the terminal point of $W$ can be recovered with probability 1 from $ \mu $. In particular, for $ d \ge 3$ the conditional law of the projection of $ W(1)$ given $ \mu $ is not $ \mu $. In dimension 2 we conjecture that the projection of $ W(1)$ cannot be recovered almost surely from $ \mu $, and show that the conditional law of the projection of $ W(1)$ given $ \mu $ is not $ m u$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, conditional distribution of a path given its occupation measure, radial projection", } @Article{Fill:2001:MTM, author = "James Fill and Clyde {Schoolfield, Jr.}", title = "Mixing Times for {Markov} Chains on Wreath Products and Related Homogeneous Spaces", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "11:1--11:22", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-84", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/84", abstract = "We develop a method for analyzing the mixing times for a quite general class of Markov chains on the complete monomial group $ G \wr S_n $ and a quite general class of Markov chains on the homogeneous space $ (G \wr S_n) / (S_r \times S_{n - r}) $. We derive an exact formula for the $ L^2 $ distance in terms of the $ L^2 $ distances to uniformity for closely related random walks on the symmetric groups $ S_j $ for $ 1 \leq j \leq n $ or for closely related Markov chains on the homogeneous spaces $ S_{i + j} / (S_i \times S_j) $ for various values of $i$ and $j$, respectively. Our results are consistent with those previously known, but our method is considerably simpler and more general.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov chain, random walk, rate of convergence to stationarity, mixing time, wreath product, Bernoulli--Laplace diffusion, complete monomial group, hyperoctahedral group, homogeneous space, M{\"o}bius inversion.", } @Article{Mikulevicius:2001:NKT, author = "R. Mikulevicius and B. Rozovskii", title = "A Note on {Krylov}'s {$ L_p $}-Theory for Systems of {SPDEs}", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "12:1--12:35", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-85", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/85", abstract = "We extend Krylov's $ L_p$-solvability theory to the Cauchy problem for systems of parabolic stochastic partial differential equations. Some additional integrability and regularity properties are also presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic partial differential equations, Cauchy problem", } @Article{Nishioka:2001:BCO, author = "Kunio Nishioka", title = "Boundary Conditions for One-Dimensional Biharmonic Pseudo Process", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "13:1--13:27", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-86", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/86", abstract = "We study boundary conditions for a stochastic pseudo processes corresponding to the biharmonic operator. The biharmonic pseudo process ({\em BPP\/} for short). is composed, in a sense, of two different particles, a monopole and a dipole. We show how an initial-boundary problems for a 4-th order parabolic differential equation can be represented by {\em BPP\/} with various boundary conditions for the two particles: killing, reflection and stopping.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Boundary conditions for biharmonic pseudo process, killing, reflection, stopping", } @Article{Miermont:2001:OAC, author = "Gr{\'e}gory Miermont", title = "Ordered Additive Coalescent and Fragmentations Associated to {L{\'e}vy} Processes with No Positive Jumps", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "14:1--14:33", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-87", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/87", abstract = "We study here the fragmentation processes that can be derived from L{\'e}vy processes with no positive jumps in the same manner as in the case of a Brownian motion (cf. Bertoin [4]). One of our motivations is that such a representation of fragmentation processes by excursion-type functions induces a particular order on the fragments which is closely related to the additivity of the coalescent kernel. We identify the fragmentation processes obtained this way as a mixing of time-reversed extremal additive coalescents by analogy with the work of Aldous and Pitman [2], and we make its semigroup explicit.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Additive-coalescent, fragmentation, L{\'e}vy processes, processes with exchangeable increments", } @Article{Jonasson:2001:DPM, author = "Johan Jonasson", title = "On Disagreement Percolation and Maximality of the Critical Value for iid Percolation", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "15:1--15:13", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-88", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/88", abstract = "Two different problems are studied:\par \begin{itemize} \item For an infinite locally finite connected graph $G$, let $ p_c(G)$ be the critical value for the existence of an infinite cluster in iid bond percolation on $G$ and let $ P_c = \sup \{ p_c(G) \colon G \text { transitive }, p_c(G) < 1 \} $. Is $ P_c < 1$ ? \item Let $G$ be transitive with $ p_c(G) < 1$, take $ p \in [0, 1]$ and let $X$ and $Y$ be iid bond percolations on $G$ with retention parameters $ (1 + p) / 2$ and $ (1 - p) / 2$ respectively. Is there a $ q < 1$ such that $ p > q$ implies that for any monotone coupling $ (X', Y')$ of $X$ and $Y$ the edges for which $ X'$ and $ Y'$ disagree form infinite connected component(s) with positive probability? Let $ p_d(G)$ be the infimum of such $q$'s (including $ q = 1$) and let $ P_d = \sup \{ p_d(G) \colon G \text { transitive }, p_c(G) < 1 \} $. Is the stronger statement $ P_d < 1$ true? On the other hand: Is it always true that $ p_d(G) > p_c (G)$ ? \end{itemize}\par It is shown that if one restricts attention to biregular planar graphs then these two problems can be treated in a similar way and all the above questions are positively answered. We also give examples to show that if one drops the assumption of transitivity, then the answer to the above two questions is no. Furthermore it is shown that for any bounded-degree bipartite graph $G$ with $ p_c(G) < 1$ one has $ p_c(G) < p_d(G)$. Problem (2) arises naturally from [6] where an example is given of a coupling of the distinct plus- and minus measures for the Ising model on a quasi-transitive graph at super-critical inverse temperature. We give an example of such a coupling on the $r$-regular tree, $ {\bf T}_r$, for $ r > 1$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coupling, Ising model, random-cluster model, transitive graph, planar graph", } @Article{DelMoral:2001:CDG, author = "P. {Del Moral} and M. Kouritzin and L. Miclo", title = "On a Class of Discrete Generation Interacting Particle Systems", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "16:1--16:26", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-89", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/89", abstract = "The asymptotic behavior of a general class of discrete generation interacting particle systems is discussed. We provide $ L_p$-mean error estimates for their empirical measure on path space and present sufficient conditions for uniform convergence of the particle density profiles with respect to the time parameter. Several examples including mean field particle models, genetic schemes and McKean's Maxwellian gases will also be given. In the context of Feynman--Kac type limiting distributions we also prove central limit theorems and we start a variance comparison for two generic particle approximating models.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Interacting particle systems, genetic algorithms, Feynman--Kac formulas, stochastic approximations, central limit theorem", } @Article{Kurtz:2001:SSF, author = "Thomas Kurtz and Richard Stockbridge", title = "Stationary Solutions and Forward Equations for Controlled and Singular Martingale Problems", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "17:1--17:52", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-90", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/90", abstract = "Stationary distributions of Markov processes can typically be characterized as probability measures that annihilate the generator in the sense that $ | \int_E A f d \mu = 0 $ for $ f \in {\cal D}(A) $; that is, for each such $ \mu $, there exists a stationary solution of the martingale problem for $A$ with marginal distribution $ \mu $. This result is extended to models corresponding to martingale problems that include absolutely continuous and singular (with respect to time) components and controls. Analogous results for the forward equation follow as a corollary.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "singular controls, stationary processes, Markov processes, martingale problems, forward equations, constrained Markov processes", } @Article{Atar:2001:IWT, author = "Rami Atar", title = "Invariant Wedges for a Two-Point Reflecting {Brownian} Motion and the ``Hot Spots'' Problem", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "18:1--18:19", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-91", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/91", abstract = "We consider domains $D$ of $ R^d$, $ d \ge 2$ with the property that there is a wedge $ V \subset R^d$ which is left invariant under all tangential projections at smooth portions of $ \partial D$. It is shown that the difference between two solutions of the Skorokhod equation in $D$ with normal reflection, driven by the same Brownian motion, remains in $V$ if it is initially in $V$. The heat equation on $D$ with Neumann boundary conditions is considered next. It is shown that the cone of elements $u$ of $ L^2 (D)$ satisfying $ u(x) - u(y) \ge 0$ whenever $ x - y \in V$ is left invariant by the corresponding heat semigroup. Positivity considerations identify an eigenfunction corresponding to the second Neumann eigenvalue as an element of this cone. For $ d = 2$ and under further assumptions, especially convexity of the domain, this eigenvalue is simple.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Reflecting Brownian motion, Neumann eigenvalue problem, convex domains", } @Article{Lambert:2001:JLA, author = "Amaury Lambert", title = "The Joint Law of Ages and Residual Lifetimes for Two Schemes of Regenerative Sets", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "19:1--19:23", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-92", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/92", abstract = "We are interested in the component intervals of the complements of a monotone sequence $ R_n \subseteq \dots \subseteq R_1 $ of regenerative sets, for two natural embeddings. One is based on Bochner's subordination, and one on the intersection of independent regenerative sets. For each scheme, we study the joint law of the so-called ages and residual lifetimes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Multivariate renewal theory, regenerative sets, subordinator, random covering intervals", } @Article{Lyne:2001:WSS, author = "Owen Lyne and David Williams", title = "Weak Solutions for a Simple Hyperbolic System", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "20:1--20:21", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-93", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/93", abstract = "The model studied concerns a simple first-order {\em hyperbolic\/} system. The solutions in which one is most interested have discontinuities which persist for all time, and therefore need to be interpreted as {\em weak\/} solutions. We demonstrate existence and uniqueness for such weak solutions, identifying a canonical `{\em exact\/}' solution which is {\em everywhere\/} defined. The direct method used is guided by the theory of measure-valued diffusions. The method is more effective than the method of characteristics, and has the advantage that it leads immediately to the McKean representation without recourse to It{\^o}'s formula. We then conduct computer studies of our model, both by integration schemes (which {\em do\/} use characteristics) and by `random simulation'.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Weak solutions, Travelling waves, Martingales, Branching processses", } @Article{Kolokoltsov:2001:SDF, author = "Vassili Kolokoltsov", title = "Small Diffusion and Fast Dying Out Asymptotics for Superprocesses as Non-{Hamiltonian} Quasiclassics for Evolution Equations", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "21:1--21:16", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-94", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/94", abstract = "The small diffusion and fast dying out asymptotics is calculated for nonlinear equations of a class of superprocesses on manifolds, and the corresponding logarithmic limit of the solution is shown to be given by a solution of a certain problem of calculus of variations with a non-additive (and non-integral) functional.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dawson--Watanabe superprocess, reaction diffusion equation, logarithmic limit, small diffusion asymptotics, curvilinear Ornstein--Uhlenbeck process", } @Article{Telcs:2001:LSG, author = "Andras Telcs", title = "Local Sub-{Gaussian} Estimates on Graphs: The Strongly Recurrent Case", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "22:1--22:33", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-95", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/95", abstract = "This paper proves upper and lower off-diagonal, sub-Gaussian transition probabilities estimates for strongly recurrent random walks under sufficient and necessary conditions. Several equivalent conditions are given showing their particular role and influence on the connection between the sub-Gaussian estimates, parabolic and elliptic Harnack inequality.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walks, potential theory, Harnack inequality, reversible Markov chains", } @Article{Benjamini:2001:RDL, author = "Itai Benjamini and Oded Schramm", title = "Recurrence of Distributional Limits of Finite Planar Graphs", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "23:1--23:13", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-96", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/96", abstract = "Suppose that $ G_j $ is a sequence of finite connected planar graphs, and in each $ G_j $ a special vertex, called the root, is chosen randomly-uniformly. We introduce the notion of a distributional limit $G$ of such graphs. Assume that the vertex degrees of the vertices in $ G_j$ are bounded, and the bound does not depend on $j$. Then after passing to a subsequence, the limit exists, and is a random rooted graph $G$. We prove that with probability one $G$ is recurrent. The proof involves the Circle Packing Theorem. The motivation for this work comes from the theory of random spherical triangulations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random triangulations, random walks, mass transport, circle packing, volume growth", } @Article{Lototsky:2001:LSP, author = "Sergey Lototsky", title = "Linear Stochastic Parabolic Equations, Degenerating on the Boundary of a Domain", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "24:1--24:14", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-97", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/97", abstract = "A class of linear degenerate second-order parabolic equations is considered in arbitrary domains. It is shown that these equations are solvable using special weighted Sobolev spaces in essentially the same way as the non-degenerate equations in $ R^d $ are solved using the usual Sobolev spaces. The main advantages of this Sobolev-space approach are less restrictive conditions on the coefficients of the equation and near-optimal space-time regularity of the solution. Unlike previous works on degenerate equations, the results cover both classical and distribution solutions and allow the domain to be bounded or unbounded without any smoothness assumptions about the boundary. An application to nonlinear filtering of diffusion processes is discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$L_p$ estimates, Weighted spaces, Nonlinear filtering", } @Article{Dawson:2001:SDS, author = "Donald Dawson and Zenghu Li and Hao Wang", title = "Superprocesses with Dependent Spatial Motion and General Branching Densities", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "25:1--25:33", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-98", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/98", abstract = "We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitrary bounded non-negative Borel function, and the superprocess is characterized by a martingale problem as a diffusion process with state space $ M({\bf R}) $, improving and extending considerably the construction of Wang (1997, 1998). It is then proved in a special case that a suitable rescaled process of the superprocess converges to the usual super Brownian motion. An extension to measure-valued branching catalysts is also discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "superprocess, interacting-branching particle system, diffusion process, martingale problem, dual process, rescaled limit, measure-valued catalyst", } @Article{Feyel:2001:FIF, author = "D. Feyel and A. {de La Pradelle}", title = "The {FBM} {It{\^o}}'s Formula Through Analytic Continuation", journal = j-ELECTRON-J-PROBAB, volume = "6", pages = "26:1--26:22", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v6-99", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/99", abstract = "The Fractional Brownian Motion can be extended to complex values of the parameter $ \alpha $ for $ \Re \alpha > {1 \over 2} $. This is a useful tool. Indeed, the obtained process depends holomorphically on the parameter, so that many formulas, as It{\^o} formula, can be extended by analytic continuation. For large values of $ \Re \alpha $, the stochastic calculus reduces to a deterministic one, so that formulas are very easy to prove. Hence they hold by analytic continuation for $ \Re \alpha \leq 1 $, containing the classical case $ \alpha = 1 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Wiener space, Sobolev space, Stochastic integral, Fractional Brownian Motion, It{\^o}'s formula", } @Article{Jacka:2001:ECN, author = "Saul Jacka and Jon Warren", title = "Examples of Convergence and Non-convergence of {Markov} Chains Conditioned Not To Die", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "1:1--1:22", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-100", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/100", abstract = "In this paper we give two examples of evanescent Markov chains which exhibit unusual behaviour on conditioning to survive for large times. In the first example we show that the conditioned processes converge vaguely in the discrete topology to a limit with a finite lifetime, but converge weakly in the Martin topology to a non-Markovian limit. In the second example, although the family of conditioned laws are tight in the Martin topology, they possess multiple limit points so that weak convergence fails altogether.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Conditioned Markov process, evanescent process, Martin boundary, Martin topology, superharmonic function, Choquet representation, star, Kolmogorov K2 chain", } @Article{Lawler:2001:OAE, author = "Gregory Lawler and Oded Schramm and Wendelin Werner", title = "One-Arm Exponent for Critical {$2$D} Percolation", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "2:1--2:13", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-101", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/101", abstract = "The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than $R$ is proved to decay like $R$ to the power $ 5 / 48$ as $R$ goes to infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Percolation, critical exponents", } @Article{Darling:2001:ILP, author = "R. Darling", title = "Intrinsic Location Parameter of a Diffusion Process", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "3:1--3:23", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-102", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/102", abstract = "For nonlinear functions $f$ of a random vector $Y$, $ E[f(Y)]$ and $ f(E[Y])$ usually differ. Consequently the mathematical expectation of $Y$ is not intrinsic: when we change coordinate systems, it is not invariant. This article is about a fundamental and hitherto neglected property of random vectors of the form $ Y = f(X(t))$, where $ X(t)$ is the value at time $t$ of a diffusion process $X$: namely that there exists a measure of location, called the ``intrinsic location parameter'' (ILP), which coincides with mathematical expectation only in special cases, and which is invariant under change of coordinate systems. The construction uses martingales with respect to the intrinsic geometry of diffusion processes, and the heat flow of harmonic mappings. We compute formulas which could be useful to statisticians, engineers, and others who use diffusion process models; these have immediate application, discussed in a separate article, to the construction of an intrinsic nonlinear analog to the Kalman Filter. We present here a numerical simulation of a nonlinear SDE, showing how well the ILP formula tracks the mean of the SDE for a Euclidean geometry.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "intrinsic location parameter, gamma-martingale, stochastic differential equation, forward--backwards SDE, harmonic map, nonlinear heat equation", } @Article{Najim:2001:CTT, author = "Jamal Najim", title = "A {Cram{\'e}r} Type Theorem for Weighted Random Variables", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "4:1--4:32", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-103", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/103", abstract = "A Large Deviation Principle (LDP) is proved for the family $ (1 / n) \sum_1^n f(x_i^n) Z_i $ where $ (1 / n) \sum_1^n \delta_{x_i^n} $ converges weakly to a probability measure on $R$ and $ (Z_i)_{i \in N}$ are $ R^d$-valued independent and identically distributed random variables having some exponential moments, i.e.,\par $$ E e^{a |Z|} < \infty $$ for some $ 0 < a < \infty $. The main improvement of this work is the relaxation of the steepness assumption concerning the cumulant generating function of the variables $ (Z_i)_{i \in N}$. In fact, G{\"a}rtner-Ellis' theorem is no longer available in this situation. As an application, we derive a LDP for the family of empirical measures $ (1 / n) \sum_1^n Z_i \delta_{x_i^n}$. These measures are of interest in estimation theory (see Gamboa et al., Csiszar et al.), gas theory (see Ellis et al., van den Berg et al.), etc. We also derive LDPs for empirical processes in the spirit of Mogul'skii's theorem. Various examples illustrate the scope of our results.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Large Deviations, empirical means, empirical measures, maximum entropy on the means", } @Article{Konig:2001:NCR, author = "Wolfgang K{\"o}nig and Neil O'Connell and S{\'e}bastien Roch", title = "Non-Colliding Random Walks, Tandem Queues, and Discrete Orthogonal Polynomial Ensembles", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "5:1--5:24", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-104", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/104", abstract = "We show that the function $ h(x) = \prod_{i < j}(x_j - x_i) $ is harmonic for any random walk in $ R^k $ with exchangeable increments, provided the required moments exist. For the subclass of random walks which can only exit the Weyl chamber $ W = \{ x \colon x_1 < x_2 < \cdots < x_k \} $ onto a point where $h$ vanishes, we define the corresponding Doob $h$-transform. For certain special cases, we show that the marginal distribution of the conditioned process at a fixed time is given by a familiar discrete orthogonal polynomial ensemble. These include the Krawtchouk and Charlier ensembles, where the underlying walks are binomial and Poisson, respectively. We refer to the corresponding conditioned processes in these cases as the Krawtchouk and Charlier processes. In [O'Connell and Yor (2001b)], a representation was obtained for the Charlier process by considering a sequence of $ M / M / 1$ queues in tandem. We present the analogue of this representation theorem for the Krawtchouk process, by considering a sequence of discrete-time $ M / M / 1$ queues in tandem. We also present related results for random walks on the circle, and relate a system of non-colliding walks in this case to the discrete analogue of the circular unitary ensemble (CUE).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Non-colliding random walks, tandem queues", } @Article{Zahle:2001:RBR, author = "Iljana Z{\"a}hle", title = "Renormalizations of Branching Random Walks in Equilibrium", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "7:1--7:57", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-106", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/106", abstract = "We study the $d$-dimensional branching random walk for $ d > 2$. This process has extremal equilibria for every intensity. We are interested in the large space scale and large space-time scale behavior of the equilibrium state. We show that the fluctuations of space and space-time averages with a non-classical scaling are Gaussian in the limit. For this purpose we use the historical process, which allows a family decomposition. To control the distribution of the families we use the concept of canonical measures and Palm distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Renormalization, branching random walk, Green's function of random walks, Palm distribution", } @Article{Luo:2001:STP, author = "S. Luo and John Walsh", title = "A Stochastic Two-Point Boundary Value Problem", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "12:1--12:32", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-111", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/111", abstract = "We investigate the two-point stochastic boundary-value problem on $ [0, 1] $: \begin{equation}\label{1} \begin{split} U'' &= f(U)\dot W + g(U, U')\\ U(0) &= \xi\\ U(1)&= \eta. \end{split} \tag{1} \end{equation} where $ \dot W $ is a white noise on $ [0, 1] $, $ \xi $ and $ \eta $ are random variables, and $f$ and $g$ are continuous real-valued functions. This is the stochastic analogue of the deterministic two point boundary-value problem, which is a classical example of bifurcation. We find that if $f$ and $g$ are affine, there is no bifurcation: for any r.v. $ \xi $ and $ \eta $, (1) has a unique solution a.s. However, as soon as $f$ is non-linear, bifurcation appears. We investigate the question of when there is either no solution whatsoever, a unique solution, or multiple solutions. We give examples to show that all these possibilities can arise. While our results involve conditions on $f$ and $g$, we conjecture that the only case in which there is no bifurcation is when $f$ is affine.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic boundary-value problems, bifurcations", } @Article{Diaconis:2002:RWT, author = "Persi Diaconis and Susan Holmes", title = "Random Walks on Trees and Matchings", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "6:1--6:17", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-105", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/105", abstract = "We give sharp rates of convergence for a natural Markov chain on the space of phylogenetic trees and dually for the natural random walk on the set of perfect matchings in the complete graph on $ 2 n $ vertices. Roughly, the results show that $ (1 / 2) n \log n $ steps are necessary and suffice to achieve randomness. The proof depends on the representation theory of the symmetric group and a bijection between trees and matchings.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov Chain, Matchings, Phylogenetic Tree, Fourier analysis, Zonal polynomials, Coagulation-Fragmentation", } @Article{Mayer-Wolf:2002:ACC, author = "Eddy Mayer-Wolf and Ofer Zeitouni and Martin Zerner", title = "Asymptotics of Certain Coagulation--Fragmentation Processes and Invariant {Poisson--Dirichlet} Measures", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "8:1--8:25", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-107", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/107", abstract = "We consider Markov chains on the space of (countable) partitions of the interval $ [0, 1] $, obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability $ \beta_m $ (if the sampled parts are distinct) or splitting the part with probability $ \beta_s $, according to a law $ \sigma $ (if the same part was sampled twice). We characterize invariant probability measures for such chains. In particular, if $ \sigma $ is the uniform measure, then the Poisson--Dirichlet law is an invariant probability measure, and it is unique within a suitably defined class of ``analytic'' invariant measures. We also derive transience and recurrence criteria for these chains.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Partitions, coagulation, fragmentation, invariant measures, Poisson--Dirichlet", } @Article{Evans:2002:ERW, author = "Steven Evans", title = "Eigenvalues of Random Wreath Products", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "9:1--9:15", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-108", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/108", abstract = "Consider a uniformly chosen element $ X_n $ of the $n$-fold wreath product $ \Gamma_n = G \wr G \wr \cdots \wr G$, where $G$ is a finite permutation group acting transitively on some set of size $s$. The eigenvalues of $ X_n$ in the natural $ s^n$-dimensional permutation representation (the composition representation) are investigated by considering the random measure $ \Xi_n$ on the unit circle that assigns mass $1$ to each eigenvalue. It is shown that if $f$ is a trigonometric polynomial, then $ \lim_{n \rightarrow \infty } P \{ \int f d \Xi_n \ne s^n \int f d \lambda \} = 0$, where $ \lambda $ is normalised Lebesgue measure on the unit circle. In particular, $ s^{-n} \Xi_n$ converges weakly in probability to $ \lambda $ as $ n \rightarrow \infty $. For a large class of test functions $f$ with non-terminating Fourier expansions, it is shown that there exists a constant $c$ and a non-zero random variable $W$ (both depending on $f$) such that $ c^{-n} \int f d \Xi_n$ converges in distribution as $ n \rightarrow \infty $ to $W$. These results have applications to Sylow $p$-groups of symmetric groups and autmorphism groups of regular rooted trees.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random permutation, random matrix, Haar measure, regular tree, Sylow, branching process, multiplicative function", } @Article{Mueller:2002:HPR, author = "Carl Mueller and Roger Tribe", title = "Hitting Properties of a Random String", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "10:1--10:29", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-109", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/109", abstract = "We consider Funaki's model of a random string taking values in $ \mathbf {R}^d $. It is specified by the following stochastic PDE,\par $$ \frac {\partial u(x)}{\partial t} = \frac {\partial^2 u(x)}{\partial x^2} + \dot {W}. $$ where $ \dot {W} = \dot {W}(x, t) $ is two-parameter white noise, also taking values in $ \mathbf {R}^d $. We find the dimensions in which the string hits points, and in which it has double points of various types. We also study the question of recurrence and transience.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Martingale, random set, strong martingale property", } @Article{Belitsky:2002:DSS, author = "Vladimir Belitsky and Gunter Sch{\"u}tz", title = "Diffusion and Scattering of Shocks in the Partially Asymmetric Simple Exclusion Process", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "11:1--11:21", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-110", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/110", abstract = "We study the behavior of shocks in the asymmetric simple exclusion process on $Z$ whose initial distribution is a product measure with a finite number of shocks. We prove that if the particle hopping rates of this process are in a particular relation with the densities of the initial measure then the distribution of this process at any time is a linear combination of shock measures of the structure similar to that of the initial distribution. The structure of this linear combination allows us to interpret this result by saying that the shocks of the initial distribution perform continuous time random walks on $Z$ interacting by the exclusion rule. We give explicit expressions for the hopping rates of these random walks. The result is derived with a help of quantum algebra technique. We made the presentation self-contained for the benefit of readers not acquainted with this approach, but interested in applying it in the study of interacting particle systems.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Asymmetric simple exclusion process, evolution of shock measures, quantum algebra", } @Article{Winter:2002:MSA, author = "Anita Winter", title = "Multiple Scale Analysis of Spatial Branching Processes under the Palm Distribution", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "13:1--13:74", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-112", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/112", abstract = "We consider two types of measure-valued branching processes on the lattice $ Z^d $. These are on the one hand side a particle system, called branching random walk, and on the other hand its continuous mass analogue, a system of interacting diffusions also called super random walk. It is known that the long-term behavior differs sharply in low and high dimensions: if $ d \leq 2 $ one gets local extinction, while, for $ d \geq 3 $, the systems tend to a non-trivial equilibrium. Due to Kallenberg's criterion, local extinction goes along with clumping around a 'typical surviving particle.' This phenomenon is called clustering. A detailed description of the clusters has been given for the corresponding processes on $ R^2 $ in Klenke (1997). Klenke proved that with the right scaling the mean number of particles over certain blocks are asymptotically jointly distributed like marginals of a system of coupled Feller diffusions, called system of tree indexed Feller diffusions, provided that the initial intensity is appropriately increased to counteract the local extinction. The present paper takes different remedy against the local extinction allowing also for state-dependent branching mechanisms. Instead of increasing the initial intensity, the systems are described under the Palm distribution. It will turn out together with the results in Klenke (1997) that the change to the Palm measure and the multiple scale analysis commute, as $ t \to \infty $. The method of proof is based on the fact that the tree indexed systems of the branching processes and of the diffusions in the limit are completely characterized by all their moments. We develop a machinery to describe the space-time moments of the superprocess effectively and explicitly.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "infinite particle system, superprocess, interacting diffusion, clustering, Palm distribution, grove indexed systems of diffusions, grove indexed systems of branching models, Kallenberg's backward tree", } @Article{Matsumoto:2002:WFS, author = "Hiroyuki Matsumoto and Setsuo Taniguchi", title = "{Wiener} Functionals of Second Order and Their {L{\'e}vy} Measures", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "14:1--14:30", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-113", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/113", abstract = "The distributions of Wiener functionals of second order are infinitely divisible. An explicit expression of the associated L{\'e}vy measures in terms of the eigenvalues of the corresponding Hilbert--Schmidt operators on the Cameron--Martin subspace is presented. In some special cases, a formula for the densities of the distributions is given. As an application of the explicit expression, an exponential decay property of the characteristic functions of the Wiener functionals is discussed. In three typical examples, complete descriptions are given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Wiener functional of second order, L{\'e}vy measure, Mellin transform, exponential decay", } @Article{Dawson:2002:MCB, author = "Donald Dawson and Alison Etheridge and Klaus Fleischmann and Leonid Mytnik and Edwin Perkins and Jie Xiong", title = "Mutually Catalytic Branching in The Plane: Infinite Measure States", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "15:1--15:61", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-114", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/114", abstract = "A two-type infinite-measure-valued population in $ R^2 $ is constructed which undergoes diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the local density of the other type. For a collision rate sufficiently small compared with the diffusion rate, the model is constructed as a pair of infinite-measure-valued processes which satisfy a martingale problem involving the collision local time of the solutions. The processes are shown to have densities at fixed times which live on disjoint sets and explode as they approach the interface of the two populations. In the long-term limit (in law), local extinction of one type is shown. Moreover the surviving population is uniform with random intensity. The process constructed is a rescaled limit of the corresponding $ Z^2$-lattice model studied by Dawson and Perkins (1998) and resolves the large scale mass-time-space behavior of that model under critical scaling. This part of a trilogy extends results from the finite-measure-valued case, whereas uniqueness questions are again deferred to the third part.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Catalyst, reactant, measure-valued branching, interactive branching, state-dependent branching, two-dimensional process, absolute continuity, self-similarity, collision measure, collision local time, martingale problem, moment equations, segregation of ty", } @Article{Alves:2002:PTF, author = "Oswaldo Alves and Fabio Machado and Serguei Popov", title = "Phase Transition for the Frog Model", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "16:1--16:21", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-115", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/115", abstract = "We study a system of simple random walks on graphs, known as {\em frog model}. This model can be described as follows: There are active and sleeping particles living on some graph. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability $ 1 - p $. When an active particle hits a sleeping particle, the latter becomes active. Phase transition results and asymptotic values for critical parameters are presented for $ Z^d $ and regular trees.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "simple random walk, critical probability, percolation", } @Article{Abraham:2002:PSF, author = "Romain Abraham and Laurent Serlet", title = "{Poisson} Snake and Fragmentation", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "17:1--17:15", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-116", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/116", abstract = "Our main object that we call the Poisson snake is a Brownian snake as introduced by Le Gall. This process has values which are trajectories of standard Poisson process stopped at some random finite lifetime with Brownian evolution. We use this Poisson snake to construct a self-similar fragmentation as introduced by Bertoin. A similar representation was given by Aldous and Pitman using the Continuum Random Tree. Whereas their proofs used approximation by discrete models, our representation allows continuous time arguments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Path-valued process, Brownian snake, Poisson process, fragmentation, coalescence, self-similarity", } @Article{Lejay:2002:CSI, author = "Antoine Lejay", title = "On the Convergence of Stochastic Integrals Driven by Processes Converging on account of a Homogenization Property", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "18:1--18:18", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-117", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/117", abstract = "We study the limit of functionals of stochastic processes for which an homogenization result holds. All these functionals involve stochastic integrals. Among them, we consider more particularly the Levy area and those giving the solutions of some SDEs. The main question is to know whether or not the limit of the stochastic integrals is equal to the stochastic integral of the limit of each of its terms. In fact, the answer may be negative, especially in presence of a highly oscillating first-order differential term. This provides us some counterexamples to the theory of good sequence of semimartingales.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic differential equations, good sequence of semimartingales, conditions UT and UCV, L{\'e}vy area", } @Article{Kolokoltsov:2002:TNE, author = "Vassili Kolokoltsov and R. L. Schilling and A. Tyukov", title = "Transience and Non-explosion of Certain Stochastic {Newtonian} Systems", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "19:1--19:19", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-118", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/118", abstract = "We give sufficient conditions for non-explosion and transience of the solution $ (x_t, p_t) $ (in dimensions $ \geq 3$) to a stochastic Newtonian system of the form\par $$ \begin {cases} d x_t = p_t \, d t, \\ d p_t = - \frac {\partial V(x_t) }{\partial x} \, d t - \frac { \partial c(x_t) }{ \partial x} \, d \xi_t, \end {cases} $$ where $ \{ \xi_t \}_{t \geq 0}$ is a $d$-dimensional L{\'e}vy process, $ d \xi_t$ is an It{\^o} differential and $ c \in C^2 (\mathbb {R}^d, \mathbb {R}^d)$, $ V \in C^2 (\mathbb {R}^d, \mathbb {R})$ such that $ V \geq 0$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "alpha-stable Levy processes; Levy processes; Non-explosion.; Stochastic Newtonian systems; Transience", } @Article{Fannjiang:2002:DLR, author = "Albert Fannjiang and Tomasz Komorowski", title = "Diffusion in Long-Range Correlated {Ornstein--Uhlenbeck} Flows", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "20:1--20:22", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-119", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/119", abstract = "We study a diffusion process with a molecular diffusion and random Markovian--Gaussian drift for which the usual (spatial) Peclet number is infinite. We introduce a temporal Peclet number and we prove that, under the finiteness of the temporal Peclet number, the laws of diffusions under the diffusive rescaling converge weakly, to the law of a Brownian motion. We also show that the effective diffusivity has a finite, nonzero limit as the molecular diffusion tends to zero.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Ornstein--Uhlenbeck flow, martingale central limit theorem, homogenization, Peclet number", } @Article{Warren:2002:NMP, author = "Jon Warren", title = "The Noise Made by a {Poisson} Snake", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "21:1--21:21", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-120", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/120", abstract = "The purpose of this article is to study a coalescing flow of sticky Brownian motions. Sticky Brownian motion arises as a weak solution of a stochastic differential equation, and the study of the flow reveals the nature of the extra randomness that must be added to the driving Brownian motion. This can be represented in terms of Poissonian marking of the trees associated with the excursions of Brownian motion. We also study the noise, in the sense of Tsirelson, generated by the flow. It is shown that this noise is not generated by any Brownian motion, even though it is predictable.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic flow, sticky Brownian motion, coalescence, stochastic differential equation, noise", } @Article{Atar:2002:SPC, author = "Rami Atar and Amarjit Budhiraja", title = "Stability Properties of Constrained Jump-Diffusion Processes", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "22:1--22:31", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-121", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/121", abstract = "We consider a class of jump-diffusion processes, constrained to a polyhedral cone $ G \subset \mathbb {R}^n $, where the constraint vector field is constant on each face of the boundary. The constraining mechanism corrects for ``attempts'' of the process to jump outside the domain. Under Lipschitz continuity of the Skorohod map $ \Gamma $, it is known that there is a cone $ {\cal C} $ such that the image $ \Gamma \phi $ of a deterministic linear trajectory $ \phi $ remains bounded if and only if $ \dot \phi \in {\cal C} $. Denoting the generator of a corresponding unconstrained jump-diffusion by $ \cal L $, we show that a key condition for the process to admit an invariant probability measure is that for $ x \in G $, $ {\cal L} \, {\rm id}(x) $ belongs to a compact subset of $ {\cal C}^o $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Jump diffusion processes. The Skorohod map. Stability cone. Harris recurrence", } @Article{Faure:2002:SNL, author = "Mathieu Faure", title = "Self-normalized Large Deviations for {Markov} Chains", journal = j-ELECTRON-J-PROBAB, volume = "7", pages = "23:1--23:31", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v7-122", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/122", abstract = "We prove a self-normalized large deviation principle for sums of Banach space valued functions of a Markov chain. Self-normalization applies to situations for which a full large deviation principle is not available. We follow the lead of Dembo and Shao [DemSha98b] who state partial large deviations principles for independent and identically distributed random sequences.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Large deviations, Markov chains, partial large deviation principles, self-normalization", } @Article{Dalang:2003:SNL, author = "Robert Dalang and Carl Mueller", title = "Some Non-Linear {S.P.D.E}'s That Are Second Order In Time", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "1:1--1:21", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-123", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/123", abstract = "We extend J. B. Walsh's theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation, and driven by spatially homogeneous Gaussian noise. For such equations, the fundamental solution can be a distribution in the sense of Schwartz, which appears as an integrand in the reformulation of the s.p.d.e. as a stochastic integral equation. Our approach provides an alternative to the Hilbert space integrals of Hilbert--Schmidt operators. We give several examples, including the beam equation and the wave equation, with nonlinear multiplicative noise terms.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic wave equation, stochastic beam equation, spatially homogeneous Gaussian noise, stochastic partial differential equations", } @Article{Hamadene:2003:RBS, author = "Said Hamad{\`e}ne and Youssef Ouknine", title = "Reflected Backward Stochastic Differential Equation with Jumps and Random Obstacle", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "2:1--2:20", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-124", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/124", abstract = "In this paper we give a solution for the one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process. We prove existence and uniqueness of the solution in using penalization and the Snell envelope theory. However both methods use a contraction in order to establish the result in the general case. Finally, we highlight the connection of such reflected BSDEs with integro-differential mixed stochastic optimal control.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Backward stochastic differential equation, penalization, Poisson point process, martingale representation theorem, integral-differential mixed control", } @Article{Cheridito:2003:FOU, author = "Patrick Cheridito and Hideyuki Kawaguchi and Makoto Maejima", title = "Fractional {Ornstein--Uhlenbeck} processes", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "3:1--3:14", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-125", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/125", abstract = "The classical stationary Ornstein--Uhlenbeck process can be obtained in two different ways. On the one hand, it is a stationary solution of the Langevin equation with Brownian motion noise. On the other hand, it can be obtained from Brownian motion by the so called Lamperti transformation. We show that the Langevin equation with fractional Brownian motion noise also has a stationary solution and that the decay of its auto-covariance function is like that of a power function. Contrary to that, the stationary process obtained from fractional Brownian motion by the Lamperti transformation has an auto-covariance function that decays exponentially.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Fractional Brownian motion, Langevin equation, Long-range dependence, Self-similar processes, Lamperti transformation", } @Article{Dawson:2003:SDM, author = "Donald Dawson and Andreas Greven", title = "State Dependent Multitype Spatial Branching Processes and their Longtime Behavior", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "4:1--4:93", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-126", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/126", abstract = "The paper focuses on spatial multitype branching systems with spatial components (colonies) indexed by a countable group, for example $ Z^d $ or the hierarchical group. As type space we allow continua and describe populations in one colony as measures on the type space. The spatial components of the system interact via migration. Instead of the classical independence assumption on the evolution of different families of the branching population, we introduce interaction between the families through a state dependent branching rate of individuals and in addition state dependent mean offspring of individuals. However for most results we consider the critical case in this work. The systems considered arise as diffusion limits of critical multiple type branching random walks on a countable group with interaction between individual families induced by a branching rate and offspring mean for a single particle, which depends on the total population at the site at which the particle in question is located.\par The main purpose of this paper is to construct the measure valued diffusions in question, characterize them via well-posed martingale problems and finally determine their longtime behavior, which includes some new features. Furthermore we determine the dynamics of two functionals of the system, namely the process of total masses at the sites and the relative weights of the different types in the colonies as system of interacting diffusions respectively time-inhomogeneous Fleming--Viot processes. This requires a detailed analysis of path properties of the total mass processes.\par In addition to the above mentioned systems of interacting measure valued processes we construct the corresponding historical processes via well-posed martingale problems. Historical processes include information on the family structure, that is, the varying degrees of relationship between individuals.\par Ergodic theorems are proved in the critical case for both the process and the historical process as well as the corresponding total mass and relative weights functionals. The longtime behavior differs qualitatively in the cases in which the symmetrized motion is recurrent respectively transient. We see local extinction in one case and honest equilibria in the other.\par This whole program requires the development of some new techniques, which should be of interest in a wider context. Such tools are dual processes in randomly fluctuating medium with singularities and coupling for systems with multi-dimensional components.\par The results above are the basis for the analysis of the large space-time scale behavior of such branching systems with interaction carried out in a forthcoming paper. In particular we study there the universality properties of the longtime behavior and of the family (or genealogical) structure, when viewed on large space and time scales.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Spatial branching processes with interaction, multitype branching processes with type-interaction, historical process, universality, coupling of multidimensional processes, coalescing random walks in singular random environment", } @Article{Kesten:2003:BRW, author = "Harry Kesten and Vladas Sidoravicius", title = "Branching Random Walk with Catalysts", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "5:1--5:51", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-127", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/127", abstract = "Shnerb et al. (2000), (2001) studied the following system of interacting particles on $ \mathbb {Z}^d $: There are two kinds of particles, called $A$-particles and $B$-particles. The $A$-particles perform continuous time simple random walks, independently of each other. The jump rate of each $A$-particle is $ D_A$. The $B$-particles perform continuous time simple random walks with jump rate $ D_B$, but in addition they die at rate $ \delta $ and a $B$-particle at $x$ at time $s$ splits into two particles at $x$ during the next $ d s$ time units with a probability $ \beta N_A(x, s)d s + o(d s)$, where $ N_A(x, s) \; (N_B(x, s))$ denotes the number of $A$-particles (respectively $B$-particles) at $x$ at time $s$. Conditionally on the $A$-system, the jumps, deaths and splittings of different $B$-particles are independent. Thus the $B$-particles perform a branching random walk, but with a birth rate of new particles which is proportional to the number of $A$-particles which coincide with the appropriate $B$-particles. One starts the process with all the $ N_A(x, 0), \, x \in \mathbb {Z}^d$, as independent Poisson variables with mean $ \mu_A$, and the $ N_B(x, 0), \, x \in \mathbb {Z}^d$, independent of the $A$-system, translation invariant and with mean $ \mu_B$.\par Shnerb et al. (2000) made the interesting discovery that in dimension 1 and 2 the expectation $ \mathbb {E} \{ N_B(x, t) \} $ tends to infinity, {\em no matter what the values of } $ \delta, \beta, D_A$, $ D_B, \mu_A, \mu_B \in (0, \infty)$ {\em are}. We shall show here that nevertheless {\em there is a phase transition in all dimensions}, that is, the system becomes (locally) extinct for large $ \delta $ but it survives for $ \beta $ large and $ \delta $ small.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching random walk, survival, extinction", } @Article{Sturm:2003:CPP, author = "Anja Sturm", title = "On Convergence of Population Processes in Random Environments to the Stochastic Heat Equation with Colored Noise", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "6:1--6:39", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-129", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/129", abstract = "We consider the stochastic heat equation with a multiplicative colored noise term on the real space for dimensions greater or equal to 1. First, we prove convergence of a branching particle system in a random environment to this stochastic heat equation with linear noise coefficients. For this stochastic partial differential equation with more general non-Lipschitz noise coefficients we show convergence of associated lattice systems, which are infinite dimensional stochastic differential equations with correlated noise terms, provided that uniqueness of the limit is known. In the course of the proof, we establish existence and uniqueness of solutions to the lattice systems, as well as a new existence result for solutions to the stochastic heat equation. The latter are shown to be jointly continuous in time and space under some mild additional assumptions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Heat equation, colored noise, stochastic partial differential equation, superprocess, weak convergence, particle representation, random environment, existence theorem", } @Article{Bottcher:2003:NPL, author = "Albrecht B{\"o}ttcher and Sergei Grudsky", title = "The Norm of the Product of a Large Matrix and a Random Vector", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "7:1--7:29", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-132", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/132", abstract = "Given a real or complex $ n \times n $ matrix $ A_n $, we compute the expected value and the variance of the random variable $ \| A_n x \|^2 / \| A_n \|^2 $, where $x$ is uniformly distributed on the unit sphere of $ R^n$ or $ C^n$. The result is applied to several classes of structured matrices. It is in particular shown that if $ A_n$ is a Toeplitz matrix $ T_n(b)$, then for large $n$ the values of $ \| A_n x \| / \| A_n \| $ cluster fairly sharply around $ \| b \|_2 / \| b \|_\infty $ if $b$ is bounded and around zero in case $b$ is unbounded.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Condition number. Matrix norm. Random vector. Toeplitz matrix", } @Article{Fleischmann:2003:CSS, author = "Klaus Fleischmann and Leonid Mytnik", title = "Competing Species Superprocesses with Infinite Variance", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "8:1--8:59", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-136", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/136", abstract = "We study pairs of interacting measure-valued branching processes (superprocesses) with alpha-stable migration and $ (1 + \beta)$-branching mechanism. The interaction is realized via some killing procedure. The collision local time for such processes is constructed as a limit of approximating collision local times. For certain dimensions this convergence holds uniformly over all pairs of such interacting superprocesses. We use this uniformity to prove existence of a solution to a competing species martingale problem under a natural dimension restriction. The competing species model describes the evolution of two populations where individuals of different types may kill each other if they collide. In the case of Brownian migration and finite variance branching, the model was introduced by Evans and Perkins (1994). The fact that now the branching mechanism does not have finite variance requires the development of new methods for handling the collision local time which we believe are of some independent interest.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Superprocess with killing, competing superprocesses, interactive superprocesses, superprocess with immigration, measure-valued branching, interactive branching, state-dependent branching, collision measure, collision local time, martingale problem", } @Article{Bai:2003:BEB, author = "Zhi-Dong Bai and Hsien-Kuei Hwang and Tsung-Hsi Tsai", title = "{Berry--Ess{\'e}en} Bounds for the Number of Maxima in Planar Regions", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "9:1--9:26", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-137", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/137", abstract = "We derive the optimal convergence rate $ O(n^{-1 / 4}) $ in the central limit theorem for the number of maxima in random samples chosen uniformly at random from the right equilateral triangle with two sides parallel to the axes, the hypotenuse with the slope $ - 1 $ and constituting the top part of the boundary of the triangle. A local limit theorem with rate is also derived. The result is then applied to the number of maxima in general planar regions (upper-bounded by some smooth decreasing curves) for which a near-optimal convergence rate to the normal distribution is established.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dominance, Maximal points, Central limit theorem, {Berry--Ess{\'e}en} bound, Local limit theorem, Method of moments", } @Article{Fitzsimmons:2003:HRM, author = "Patrick Fitzsimmons and Ronald Getoor", title = "Homogeneous Random Measures and Strongly Supermedian Kernels of a {Markov} Process", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "10:1--10:54", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-142", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/142", abstract = "The potential kernel of a positive {\em left} additive functional (of a strong Markov process $X$) maps positive functions to {\em strongly supermedian} functions and satisfies a variant of the classical {\em domination principle} of potential theory. Such a kernel $V$ is called a {\em regular strongly supermedian } kernel in recent work of L. Beznea and N. Boboc. We establish the converse: Every regular strongly supermedian kernel $V$ is the potential kernel of a random measure homogeneous on $ [0, \infty [$. Under additional finiteness conditions such random measures give rise to left additive functionals. We investigate such random measures, their potential kernels, and their associated characteristic measures. Given a left additive functional $A$ (not necessarily continuous), we give an explicit construction of a simple Markov process $Z$ whose resolvent has initial kernel equal to the potential kernel $ U_{\! A}$. The theory we develop is the probabilistic counterpart of the work of Beznea and Boboc. Our main tool is the Kuznetsov process associated with $X$ and a given excessive measure $m$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Homogeneous random measure, additive functional, Kuznetsov measure, potential kernel, characteristic measure, strongly supermedian, smooth measure", } @Article{Zhou:2003:CBC, author = "Xiaowen Zhou", title = "Clustering Behavior of a Continuous-Sites Stepping-Stone Model with {Brownian} Migration", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "11:1--11:15", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-141", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/141", abstract = "Clustering behavior is studied for a continuous-sites stepping-stone model with Brownian migration. It is shown that, if the model starts with the same mixture of different types of individuals over each site, then it will evolve in a way such that the site space is divided into disjoint intervals where only one type of individuals appear in each interval. Those intervals (clusters) are growing as time $t$ goes to infinity. The average size of the clusters at a fixed time $t$ is of the order of square root of $t$. Clusters at different times or sites are asymptotically independent as the difference of either the times or the sites goes to infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "clustering; coalescing Brownian motion; stepping-stone model", } @Article{Marquez-Carreras:2003:LDP, author = "David Marquez-Carreras and Monica Sarra", title = "Large Deviation Principle for a Stochastic Heat Equation With Spatially Correlated Noise", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "12:1--12:39", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-146", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/146", abstract = "In this paper we prove a large deviation principle (LDP) for a perturbed stochastic heat equation defined on $ [0, T] \times [0, 1]^d $. This equation is driven by a Gaussian noise, white in time and correlated in space. Firstly, we show the Holder continuity for the solution of the stochastic heat equation. Secondly, we check that our Gaussian process satisfies an LDP and some requirements on the skeleton of the solution. Finally, we prove the called Freidlin--Wentzell inequality. In order to obtain all these results we need precise estimates of the fundamental solution of this equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic partial differential equation, stochastic heat equation, Gaussian noise, large deviation principle", } @Article{Gao:2003:LTH, author = "Fuchang Gao and Jan Hannig and Tzong-Yow Lee and Fred Torcaso", title = "{Laplace} Transforms via {Hadamard} Factorization", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "13:1--13:20", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-151", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/151", abstract = "In this paper we consider the Laplace transforms of some random series, in particular, the random series derived as the squared $ L_2 $ norm of a Gaussian stochastic process. Except for some special cases, closed form expressions for Laplace transforms are, in general, rarely obtained. It is the purpose of this paper to show that for many Gaussian random processes the Laplace transform can be expressed in terms of well understood functions using complex-analytic theorems on infinite products, in particular, the Hadamard Factorization Theorem. Together with some tools from linear differential operators, we show that in many cases the Laplace transforms can be obtained with little work. We demonstrate this on several examples. Of course, once the Laplace transform is known explicitly one can easily calculate the corresponding exact $ L_2 $ small ball probabilities using Sytaja Tauberian theorem. Some generalizations are mentioned.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Small ball probability, Laplace Transforms, Hadamard's factorization theorem", } @Article{Tudor:2003:IFL, author = "Ciprian Tudor and Frederi Viens", title = "{It{\^o}} Formula and Local Time for the Fractional {Brownian} Sheet", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "14:1--14:31", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-155", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/155", abstract = "Using the techniques of the stochastic calculus of variations for Gaussian processes, we derive an It{\^o} formula for the fractional Brownian sheet with Hurst parameters bigger than $ 1 / 2 $. As an application, we give a stochastic integral representation for the local time of the fractional Brownian sheet.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractional Brownian sheet, It{\^o} formula, local time, Tanaka formula, Malliavin calculus", } @Article{Dembo:2003:BMC, author = "Amir Dembo and Yuval Peres and Jay Rosen", title = "{Brownian} Motion on Compact Manifolds: Cover Time and Late Points", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "15:1--15:14", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-139", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/139", abstract = "Let $M$ be a smooth, compact, connected Riemannian manifold of dimension $ d > 2$ and without boundary. Denote by $ T(x, r)$ the hitting time of the ball of radius $r$ centered at $x$ by Brownian motion on $M$. Then, $ C_r(M) = \sup_{x \in M} T(x, r)$ is the time it takes Brownian motion to come within $r$ of all points in $M$. We prove that $ C_r(M) / (r^{2 - d}| \log r|)$ tends to $ \gamma_d V(M)$ almost surely as $ r \to 0$, where $ V(M)$ is the Riemannian volume of $M$. We also obtain the ``multi-fractal spectrum'' $ f(\alpha)$ for ``late points'', i.e., the dimension of the set of $ \alpha $-late points $x$ in $M$ for which $ \limsup_{r \to 0} T(x, r) / (r^{2 - d}| \log r|) = \alpha > 0$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, manifold, cover time, Wiener sausage", } @Article{Budhiraja:2003:LDE, author = "Amarjit Budhiraja and Paul Dupuis", title = "Large Deviations for the Emprirical Measures of Reflecting {Brownian} Motion and Related Constrained Processes in {$ R_+ $}", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "16:1--16:46", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-154", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/154", abstract = "We consider the large deviations properties of the empirical measure for one dimensional constrained processes, such as reflecting Brownian motion, the M/M/1 queue, and discrete time analogues. Because these processes do not satisfy the strong stability assumptions that are usually assumed when studying the empirical measure, there is significant probability (from the perspective of large deviations) that the empirical measure charges the point at infinity. We prove the large deviation principle and identify the rate function for the empirical measure for these processes. No assumption of any kind is made with regard to the stability of the underlying process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov process, constrained process, large deviations, empirical measure, stability, reflecting Brownian motion", } @Article{Delmas:2003:CML, author = "Jean-Fran{\c{c}}ois Delmas", title = "Computation of Moments for the Length of the One-Dimensional {ISE} Support", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "17:1--17:15", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-161", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/161", abstract = "We consider in this paper the support $ [L', R'] $ of the one dimensional Integrated Super Brownian Excursion. We determine the distribution of $ (R', L') $ through a modified Laplace transform. Then we give an explicit value for the first two moments of $ R' $ as well as the covariance of $ R' $ and $ {L'} $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian snake; ISE", } @Article{Gradinaru:2003:AFS, author = "Mihai Gradinaru and Ivan Nourdin", title = "Approximation at First and Second Order of $m$-order Integrals of the Fractional {Brownian} Motion and of Certain Semimartingales", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "18:1--18:26", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-166", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/166", abstract = "Let $X$ be the fractional Brownian motion of any Hurst index $ H \in (0, 1)$ (resp. a semimartingale) and set $ \alpha = H$ (resp. $ \alpha = \frac {1}{2}$). If $Y$ is a continuous process and if $m$ is a positive integer, we study the existence of the limit, as $ \varepsilon \rightarrow 0$, of the approximations\par $$ I_{\varepsilon }(Y, X) := \left \{ \int_0^t Y_s \left (\frac {X_{s + \varepsilon } - X_s}{\varepsilon^{\alpha }} \right)^m d s, \, t \geq 0 \right \} $$ of $m$-order integral of $Y$ with respect to $X$. For these two choices of $X$, we prove that the limits are almost sure, uniformly on each compact interval, and are in terms of the $m$-th moment of the Gaussian standard random variable. In particular, if $m$ is an odd integer, the limit equals to zero. In this case, the convergence in distribution, as $ \varepsilon \rightarrow 0$, of $ \varepsilon^{- \frac {1}{2}} I_{\varepsilon }(1, X)$ is studied. We prove that the limit is a Brownian motion when $X$ is the fractional Brownian motion of index $ H \in (0, \frac {1}{2}]$, and it is in term of a two dimensional standard Brownian motion when $X$ is a semimartingale.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Maejima:2003:LMS, author = "Makoto Maejima and Kenji Yamamoto", title = "Long-Memory Stable {Ornstein--Uhlenbeck} Processes", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "19:1--19:18", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-168", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/168", abstract = "The solution of the Langevin equation driven by a L{\'e}vy process noise has been well studied, under the name of Ornstein--Uhlenbeck type process. It is a stationary Markov process. When the noise is fractional Brownian motion, the covariance of the stationary solution process has been studied by the first author with different coauthors. In the present paper, we consider the Langevin equation driven by a linear fractional stable motion noise, which is a selfsimilar process with long-range dependence but does not have finite variance, and we investigate the dependence structure of the solution process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Lachal:2003:DST, author = "Aime Lachal", title = "Distributions of Sojourn Time, Maximum and Minimum for Pseudo-Processes Governed by Higher-Order Heat-Type Equations", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "20:1--20:53", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-178", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/178", abstract = "The higher-order heat-type equation $ \partial u / \partial t = \pm \partial^n u / \partial x^n $ has been investigated by many authors. With this equation is associated a pseudo-process $ (X_t)_{t \ge 0} $ which is governed by a signed measure. In the even-order case, Krylov (1960) proved that the classical arc-sine law of Paul Levy for standard Brownian motion holds for the pseudo-process $ (X_t)_{t \ge 0} $, that is, if $ T_t $ is the sojourn time of $ (X_t)_{t \ge 0} $ in the half line $ (0, + \infty) $ up to time $t$, then $ P(T_t \in d s) = \frac {ds}{\pi \sqrt {s(t - s)}}$, $ 0 < s < t$. Orsingher (1991) and next Hochberg and Orsingher (1994) obtained a counterpart to that law in the odd cases $ n = 3, 5, 7.$ Actually Hochberg and Orsingher (1994) proposed a more or less explicit expression for that new law in the odd-order general case and conjectured a quite simple formula for it. The distribution of $ T_t$ subject to some conditioning has also been studied by Nikitin \& Orsingher (2000) in the cases $ n = 3, 4.$ In this paper, we prove that the conjecture of Hochberg and Orsingher (1994) is true and we extend the results of Nikitin \& Orsingher for any integer $n$. We also investigate the distributions of maximal and minimal functionals of $ (X_t)_{t \ge 0}$, as well as the distribution of the last time before becoming definitively negative up to time $t$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Gao:2003:CTS, author = "Fuchang Gao and Jan Hannig and Fred Torcaso", title = "Comparison Theorems for Small Deviations of Random Series", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "21:1--21:17", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-147", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/147", abstract = "Let $ {\xi_n} $ be a sequence of i.i.d. positive random variables with common distribution function $ F(x) $. Let $ {a_n} $ and $ {b_n} $ be two positive non-increasing summable sequences such that $ {\prod_{n = 1}^{\infty }(a_n / b_n)} $ converges. Under some mild assumptions on $F$, we prove the following comparison\par $$ P \left (\sum_{n = 1}^{\infty }a_n \xi_n \leq \varepsilon \right) \sim \left (\prod_{n = 1}^{\infty } \frac {b_n}{a_n} \right)^{- \alpha } P \left (\sum_{n = 1}^{\infty }b_n \xi_n \leq \varepsilon \right), $$ where\par $$ { \alpha = \lim_{x \to \infty } \frac {\log F(1 / x)}{\log x}} < 0 $$ is the index of variation of $ F(1 / \cdot)$. When applied to the case $ \xi_n = |Z_n|^p$, where $ Z_n$ are independent standard Gaussian random variables, it affirms a conjecture of Li cite {Li1992a}.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "small deviation, random series, bounded variation", } @Article{Appleby:2003:EAS, author = "John Appleby and Alan Freeman", title = "Exponential Asymptotic Stability of Linear {It{\^o}--Volterra} Equation with Damped Stochastic Perturbations", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "22:1--22:22", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-179", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/179", abstract = "This paper studies the convergence rate of solutions of the linear It{\^o}-Volterra equation\par $$ d X(t) = \left (A X(t) + \int_0^t K(t - s)X(s), d s \right) \, d t + \Sigma (t) \, d W(t) \tag {1} $$ where $K$ and $ \Sigma $ are continuous matrix-valued functions defined on $ \mathbb {R}^+$, and $ (W(t))_{t \geq 0}$ is a finite-dimensional standard Brownian motion. It is shown that when the entries of $K$ are all of one sign on $ \mathbb {R}^+$, that (i) the almost sure exponential convergence of the solution to zero, (ii) the $p$-th mean exponential convergence of the solution to zero (for all $ p > 0$), and (iii) the exponential integrability of the entries of the kernel $K$, the exponential square integrability of the entries of noise term $ \Sigma $, and the uniform asymptotic stability of the solutions of the deterministic version of (1) are equivalent. The paper extends a result of Murakami which relates to the deterministic version of this problem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Volkov:2003:ERW, author = "Stanislav Volkov", title = "Excited Random Walk on Trees", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "23:1--23:15", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-180", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/180", abstract = "We consider a nearest-neighbor stochastic process on a rooted tree $G$ which goes toward the root with probability $ 1 - \varepsilon $ when it visits a vertex for the first time. At all other times it behaves like a simple random walk on $G$. We show that for all $ \varepsilon \ge 0$ this process is transient. Also we consider a generalization of this process and establish its transience in {\em some} cases.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ocone:2004:DVC, author = "Daniel Ocone and Ananda Weerasinghe", title = "Degenerate Variance Control in the One-dimensional Stationary Case", journal = j-ELECTRON-J-PROBAB, volume = "8", pages = "24:27", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v8-181", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/181", abstract = "We study the problem of stationary control by adaptive choice of the diffusion coefficient in the case that control degeneracy is allowed and the drift admits a unique, asymptotically stable equilibrium point. We characterize the optimal value and obtain it as an Abelian limit of optimal discounted values and as a limiting average of finite horizon optimal values, and we also characterize the optimal stationary strategy. In the case of linear drift, the optimal stationary value is expressed in terms of the solution of an optimal stopping problem. We generalize the above results to allow unbounded cost functions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stationary control, degenerate variance control; stochastic control", } @Article{Kozma:2004:AED, author = "Gady Kozma and Ehud Schreiber", title = "An asymptotic expansion for the discrete harmonic potential", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "1:1--1:17", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-170", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/170", abstract = "We give two algorithms that allow to get arbitrary precision asymptotics for the harmonic potential of a random walk.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Barbour:2004:NUB, author = "Andrew Barbour and Kwok Choi", title = "A non-uniform bound for translated {Poisson} approximation", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "2:18--2:36", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-182", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/182", abstract = "Let $ X_1, \ldots, X_n $ be independent, integer valued random variables, with $ p^{\text {th}} $ moments, $ p > 2 $, and let $W$ denote their sum. We prove bounds analogous to the classical non-uniform estimates of the error in the central limit theorem, but now, for approximation of $ {\cal L}(W)$ by a translated Poisson distribution. The advantage is that the error bounds, which are often of order no worse than in the classical case, measure the accuracy in terms of total variation distance. In order to have good approximation in this sense, it is necessary for $ {\cal L}(W)$ to be sufficiently smooth; this requirement is incorporated into the bounds by way of a parameter $ \alpha $, which measures the average overlap between $ {\cal L}(X_i)$ and $ {\cal L}(X_i + 1), 1 \leq i \leq n$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "non-uniform bounds; Stein's method; total variation; translated Poisson approximation", } @Article{Aldous:2004:BBA, author = "David Aldous and Gregory Miermont and Jim Pitman", title = "{Brownian} Bridge Asymptotics for Random $p$-Mappings", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "3:37--3:56", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-186", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/186", abstract = "The Joyal bijection between doubly-rooted trees and mappings can be lifted to a transformation on function space which takes tree-walks to mapping-walks. Applying known results on weak convergence of random tree walks to Brownian excursion, we give a conceptually simpler rederivation of the Aldous--Pitman (1994) result on convergence of uniform random mapping walks to reflecting Brownian bridge, and extend this result to random $p$-mappings.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian bridge, Brownian excursion, Joyal map, random mapping, random tree, weak convergence", } @Article{Haas:2004:GSS, author = "B{\'e}n{\'e}dicte Haas and Gr{\'e}gory Miermont", title = "The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "4:57--4:97", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-187", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/187", abstract = "We encode a certain class of stochastic fragmentation processes, namely self-similar fragmentation processes with a negative index of self-similarity, into a metric family tree which belongs to the family of Continuum Random Trees of Aldous. When the splitting times of the fragmentation are dense near 0, the tree can in turn be encoded into a continuous height function, just as the Brownian Continuum Random Tree is encoded in a normalized Brownian excursion. Under mild hypotheses, we then compute the Hausdorff dimensions of these trees, and the maximal H{\"o}lder exponents of the height functions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Mueller:2004:SPA, author = "Carl Mueller and Roger Tribe", title = "A Singular Parabolic {Anderson} Model", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "5:98--5:144", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-189", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/189", abstract = "We consider the heat equation with a singular random potential term. The potential is Gaussian with mean 0 and covariance given by a small constant times the inverse square of the distance. Solutions exist as singular measures, under suitable assumptions on the initial conditions and for sufficiently small noise. We investigate various properties of the solutions using such tools as scaling, self-duality and moment formulae. This model lies on the boundary between nonexistence and smooth solutions. It gives a new model, other than the superprocess, which has measure-valued solutions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic partial differential equations", } @Article{Fernandez:2004:CCC, author = "Roberto Fernandez and Gregory Maillard", title = "Chains with Complete Connections and One-Dimensional {Gibbs} Measures", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "6:145--6:176", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-149", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/149", abstract = "We discuss the relationship between one-dimensional Gibbs measures and discrete-time processes (chains). We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic process to define a Gibbs measure and vice versa. Our conditions generalize well known equivalence results between ergodic Markov chains and fields, as well as the known Gibbsian character of processes with exponential continuity rate. Our arguments are purely probabilistic; they are based on the study of regular systems of conditional probabilities (specifications). Furthermore, we discuss the equivalence of uniqueness criteria for chains and fields and we establish bounds for the continuity rates of the respective systems of finite-volume conditional probabilities. As an auxiliary result we prove a (re)construction theorem for specifications starting from single-site conditioning, which applies in a more general setting (general spin space, specifications not necessarily Gibbsian).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Discrete-time processes, Chains with complete connections, Gibbs measures, Markov chains", } @Article{Ledoux:2004:DOS, author = "Michel Ledoux", title = "Differential Operators and Spectral Distributions of Invariant Ensembles from the Classical Orthogonal Polynomials. {The} Continuous Case", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "7:177--7:208", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-191", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/191", abstract = "Following the investigation by U. Haagerup and S. Thorbjornsen, we present a simple differential approach to the limit theorems for empirical spectral distributions of complex random matrices from the Gaussian, Laguerre and Jacobi Unitary Ensembles. In the framework of abstract Markov diffusion operators, we derive by the integration by parts formula differential equations for Laplace transforms and recurrence equations for moments of eigenfunction measures. In particular, a new description of the equilibrium measures as adapted mixtures of the universal arcsine law with an independent uniform distribution is emphasized. The moment recurrence relations are used to describe sharp, non asymptotic, small deviation inequalities on the largest eigenvalues at the rate given by the Tracy--Widom asymptotics.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Doney:2004:STB, author = "Ronald Doney", title = "Small-time Behaviour of {L{\'e}vy} Processes", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "8:209--8:229", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-193", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/193", abstract = "In this paper a neccessary and sufficient condition is established for the probability that a L{\'e}vy process is positive at time $t$ to tend to 1 as $t$ tends to 0. This condition is expressed in terms of the characteristics of the process, and is also shown to be equivalent to two probabilistic statements about the behaviour of the process for small time $t$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Alabert:2004:SDE, author = "Aureli Alabert and Miguel Angel Marmolejo", title = "Stochastic differential equations with boundary conditions driven by a {Poisson} noise", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "9:230--254", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-157", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/157", abstract = "We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when the coefficients are linear, we give an explicit form of the solution and study the reciprocal process property.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "boundary conditions; Poisson noise; reciprocal processes; stochastic differential equations", } @Article{Garet:2004:PTS, author = "Olivier Garet", title = "Percolation Transition for Some Excursion Sets", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "10:255--10:292", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-196", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/196", abstract = "We consider a random field $ (X_n)_{n \in \mathbb {Z}^d} $ and investigate when the set $ A_h = \{ k \in \mathbb {Z}^d; \vert X_k \vert \ge h \} $ has infinite clusters. The main problem is to decide whether the critical level\par $$ h_c = \sup \{ h \in R \colon P(A_h \text { has an infinite cluster }) > 0 \} $$ is neither $0$ nor $ + \infty $. Thus, we say that a percolation transition occurs. In a first time, we show that weakly dependent Gaussian fields satisfy to a well-known criterion implying the percolation transition. Then, we introduce a concept of percolation along reasonable paths and therefore prove a phenomenon of percolation transition for reasonable paths even for strongly dependent Gaussian fields. This allows to obtain some results of percolation transition for oriented percolation. Finally, we study some Gibbs states associated to a perturbation of a ferromagnetic quadratic interaction. At first, we show that a transition percolation occurs for superstable potentials. Next, we go to the critical case and show that a transition percolation occurs for directed percolation when $ d \ge 4$. We also note that the assumption of ferromagnetism can be relaxed when we deal with Gaussian Gibbs measures, i.e., when there is no perturbation of the quadratic interaction.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kurkova:2004:ISC, author = "Irina Kurkova and Serguei Popov and M. Vachkovskaia", title = "On Infection Spreading and Competition between Independent Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "11:293--11:315", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-197", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/197", abstract = "We study the models of competition and spreading of infection for infinite systems of independent random walks. For the competition model, we investigate the question whether one of the spins prevails with probability one. For the infection spreading, we give sufficient conditions for recurrence and transience (i.e., whether the origin will be visited by infected particles infinitely often a.s.).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Dawson:2004:HEB, author = "Donald Dawson and Luis Gorostiza and Anton Wakolbinger", title = "Hierarchical Equilibria of Branching Populations", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "12:316--12:381", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-200", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/200", abstract = "The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group $ \Omega_N $ consisting of families of individuals undergoing critical branching random walk and in addition these families also develop according to a critical branching process. Strong transience of the random walk guarantees existence of an equilibrium for this two-level branching system. In the limit $ N \to \infty $ (called the {\em hierarchical mean field limit}), the equilibrium aggregated populations in a nested sequence of balls $ B^{(N)}_\ell $ of hierarchical radius $ \ell $ converge to a backward Markov chain on $ \mathbb {R_+} $. This limiting Markov chain can be explicitly represented in terms of a cascade of subordinators which in turn makes possible a description of the genealogy of the population.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Multilevel branching, hierarchical mean-field limit, strong transience, genealogy", } @Article{Kendall:2004:CIK, author = "Wilfrid Kendall and Catherine Price", title = "Coupling Iterated {Kolmogorov} Diffusions", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "13:382--13:410", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-201", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/201", abstract = "The {\em Kolmogorov-1934 diffusion} is the two-dimensional diffusion generated by real Brownian motion and its time integral. In this paper we construct successful co-adapted couplings for iterated Kolmogorov diffusions defined by adding iterated time integrals as further components to the original Kolmogorov diffusion. A Laplace-transform argument shows it is not possible successfully to couple all iterated time integrals at once; however we give an explicit construction of a successful co-adapted coupling method for Brownian motion, its time integral, and its twice-iterated time integral; and a more implicit construction of a successful co-adapted coupling method which works for finite sets of iterated time integrals.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{vonRenesse:2004:ICR, author = "Max-K. von Renesse", title = "Intrinsic Coupling on {Riemannian} Manifolds and Polyhedra", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "14:411--14:435", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-205", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/205", abstract = "Starting from a central limit theorem for geometric random walks we give an elementary construction of couplings between Brownian motions on Riemannian manifolds. This approach shows that cut locus phenomena are indeed inessential for Kendall's and Cranston's stochastic proof of gradient estimates for harmonic functions on Riemannian manifolds with lower curvature bounds. Moreover, since the method is based on an asymptotic quadruple inequality and a central limit theorem only it may be extended to certain non smooth spaces which we illustrate by the example of Riemannian polyhedra. Here we also recover the classical heat kernel gradient estimate which is well known from the smooth setting.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central Limit Theorem; Coupling; Gradient Estimates", } @Article{Loewe:2004:RMR, author = "Matthias Loewe and Heinrich Matzinger and Franz Merkl", title = "Reconstructing a Multicolor Random Scenery seen along a Random Walk Path with Bounded Jumps", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "15:436--15:507", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-206", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/206", abstract = "Kesten noticed that the scenery reconstruction method proposed by Matzinger in his PhD thesis relies heavily on the skip-free property of the random walk. He asked if one can still reconstruct an i.i.d. scenery seen along the path of a non-skip-free random walk. In this article, we positively answer this question. We prove that if there are enough colors and if the random walk is recurrent with at most bounded jumps, and if it can reach every integer, then one can almost surely reconstruct almost every scenery up to translations and reflections. Our reconstruction method works if there are more colors in the scenery than possible single steps for the random walk.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "ergodic theory; jumps; random walk; Scenery reconstruction; stationary processes", } @Article{Barral:2004:MAC, author = "Julien Barral and Jacques V{\'e}hel", title = "Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "16:508--16:543", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-208", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/208", abstract = "We consider a family of stochastic processes built from infinite sums of independent positive random functions on $ R_+ $. Each of these functions increases linearly between two consecutive negative jumps, with the jump points following a Poisson point process on $ R_+ $. The motivation for studying these processes stems from the fact that they constitute simplified models for TCP traffic on the Internet. Such processes bear some analogy with L{\'e}vy processes, but they are more complex in the sense that their increments are neither stationary nor independent. Nevertheless, we show that their multifractal behavior is very much the same as that of certain L{\'e}vy processes. More precisely, we compute the Hausdorff multifractal spectrum of our processes, and find that it shares the shape of the spectrum of a typical L{\'e}vy process. This result yields a theoretical basis to the empirical discovery of the multifractal nature of TCP traffic.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Shao:2004:ADB, author = "Qi-Man Shao and Chun Su and Gang Wei", title = "Asymptotic Distributions and {Berry--Ess{\'e}en} Bounds for Sums of Record Values", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "17:544--17:559", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-210", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/210", abstract = "Let $ \{ U_n, n \geq 1 \} $ be independent uniformly distributed random variables, and $ \{ Y_n, n \geq 1 \} $ be independent and identically distributed non-negative random variables with finite third moments. Denote $ S_n = \sum_{i = 1}^n Y_i $ and assume that $ (U_1, \cdots, U_n) $ and $ S_{n + 1} $ are independent for every fixed $n$. In this paper we obtain {Berry--Ess{\'e}en} bounds for $ \sum_{i = 1}^n \psi (U_i S_{n + 1})$, where $ \psi $ is a non-negative function. As an application, we give {Berry--Ess{\'e}en} bounds and asymptotic distributions for sums of record values.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kouritzin:2004:NFR, author = "Michael Kouritzin and Wei Sun and Jie Xiong", title = "Nonliner Filtering for Reflecting Diffusions in Random Environments via Nonparametric Estimation", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "18:560--18:574", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-214", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See erratum \cite{Kouritzin:2017:ENF}.", URL = "http://ejp.ejpecp.org/article/view/214", abstract = "We study a nonlinear filtering problem in which the signal to be estimated is a reflecting diffusion in a random environment. Under the assumption that the observation noise is independent of the signal, we develop a nonparametric functional estimation method for finding workable approximate solutions to the conditional distributions of the signal state. Furthermore, we show that the pathwise average distance, per unit time, of the approximate filter from the optimal filter is asymptotically small in time. Also, we use simulations based upon a particle filter algorithm to show the efficiency of the method.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bertoin:2004:ALN, author = "Jean Bertoin and Alexander Gnedin", title = "Asymptotic Laws for Nonconservative Self-similar Fragmentations", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "19:575--19:593", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-215", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/215", abstract = "We consider a self-similar fragmentation process in which the generic particle of mass $x$ is replaced by the offspring particles at probability rate $ x^\alpha $, with positive parameter $ \alpha $. The total of offspring masses may be both larger or smaller than $x$ with positive probability. We show that under certain conditions the typical mass in the ensemble is of the order $ t^{-1 / \alpha }$ and that the empirical distribution of masses converges to a random limit which we characterise in terms of the reproduction law.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Nualart:2004:LSM, author = "Eulalia Nualart and Thomas Mountford", title = "Level Sets of Multiparameter {Brownian} Motions", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "20:594--20:614", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-169", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/169", abstract = "We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that $ \phi (r) = r^{N - d / 2} (\log \log (\frac {1}{r}))^{d / 2} $ is the exact Hausdorff measure function for the zero level set of an $N$-parameter $d$-dimensional additive Brownian motion. We extend this result to a natural multiparameter version of Taylor and Wendel's theorem on the relationship between Brownian local time and the Hausdorff $ \phi $-measure of the zero set.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "additive Brownian motion; Hausdorff measure; level sets; Local times", } @Article{Krylov:2004:QIS, author = "N. V. Krylov", title = "Quasiderivatives and Interior Smoothness of Harmonic Functions Associated with Degenerate Diffusion Processes", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "21:615--21:633", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-219", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/219", abstract = "Proofs and two applications of two general results are given concerning the problem of establishing interior smoothness of probabilistic solutions of elliptic degenerate equations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bass:2004:CSD, author = "Richard Bass and Edwin Perkins", title = "Countable Systems of Degenerate Stochastic Differential Equations with Applications to Super-{Markov} Chains", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "22:634--22:673", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-222", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/222", abstract = "We prove well-posedness of the martingale problem for an infinite-dimensional degenerate elliptic operator under appropriate H{\"o}lder continuity conditions on the coefficients. These martingale problems include large population limits of branching particle systems on a countable state space in which the particle dynamics and branching rates may depend on the entire population in a H{\"o}lder fashion. This extends an approach originally used by the authors in finite dimensions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Denis:2004:GAR, author = "Laurent Denis and L. Stoica", title = "A General Analytical Result for Non-linear {SPDE}'s and Applications", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "23:674--23:709", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-223", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/223", abstract = "Using analytical methods, we prove existence uniqueness and estimates for s.p.d.e. of the type\par $$ d u_t + A u_t d t + f (t, u_t) d t + R g(t, u_t) d t = h(t, x, u_t) d B_t, $$ where $A$ is a linear non-negative self-adjoint (unbounded) operator, $f$ is a nonlinear function which depends on $u$ and its derivatives controlled by $ \sqrt {A} u$, $ R g$ corresponds to a nonlinearity involving $u$ and its derivatives of the same order as $ A u$ but of smaller magnitude, and the right term contains a noise involving a $d$-dimensional Brownian motion multiplied by a non-linear function. We give a neat condition concerning the magnitude of these nonlinear perturbations. We also mention a few examples and, in the case of a diffusion generator, we give a double stochastic interpretation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{vanderHofstad:2004:GSC, author = "Remco van der Hofstad and Akira Sakai", title = "{Gaussian} Scaling for the Critical Spread-out Contact Process above the Upper Critical Dimension", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "24:710--24:769", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-224", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/224", abstract = "We consider the critical spread-out contact process in $ Z^d $ with $ d \geq 1 $, whose infection range is denoted by $ L \geq 1 $. The two-point function $ \tau_t(x) $ is the probability that $ x \in Z^d $ is infected at time $t$ by the infected individual located at the origin $ o \in Z^d$ at time 0. We prove Gaussian behaviour for the two-point function with $ L \geq L_0$ for some finite $ L_0 = L_0 (d)$ for $ d > 4$. When $ d \leq 4$, we also perform a local mean-field limit to obtain Gaussian behaviour for $ \tau_{ tT}(x)$ with $ t > 0$ fixed and $ T \to \infty $ when the infection range depends on $T$ in such a way that $ L_T = L T^b$ for any $ b > (4 - d) / 2 d$.\par The proof is based on the lace expansion and an adaptation of the inductive approach applied to the discretized contact process. We prove the existence of several critical exponents and show that they take on their respective mean-field values. The results in this paper provide crucial ingredients to prove convergence of the finite-dimensional distributions for the contact process towards those for the canonical measure of super-Brownian motion, which we defer to a sequel of this paper.\par The results in this paper also apply to oriented percolation, for which we reprove some of the results in \cite{hs01} and extend the results to the local mean-field setting described above when $ d \leq 4$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Berestycki:2004:EFC, author = "Julien Berestycki", title = "Exchangeable Fragmentation--Coalescence Processes and their Equilibrium Measures", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "25:770--25:824", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-227", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/227", abstract = "We define and study a family of Markov processes with state space the compact set of all partitions of $N$ that we call exchangeable fragmentation-coalescence processes. They can be viewed as a combination of homogeneous fragmentation as defined by Bertoin and of homogeneous coalescence as defined by Pitman and Schweinsberg or M{\"o}hle and Sagitov. We show that they admit a unique invariant probability measure and we study some properties of their paths and of their equilibrium measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Peres:2004:MTR, author = "Yuval Peres and David Revelle", title = "Mixing Times for Random Walks on Finite Lamplighter Groups", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "26:825--26:845", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-198", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/198", abstract = "Given a finite graph $G$, a vertex of the lamplighter graph $ G^\diamondsuit = \mathbb {Z}_2 \wr G$ consists of a zero-one labeling of the vertices of $G$, and a marked vertex of $G$. For transitive $G$ we show that, up to constants, the relaxation time for simple random walk in $ G^\diamondsuit $ is the maximal hitting time for simple random walk in $G$, while the mixing time in total variation on $ G^\diamondsuit $ is the expected cover time on $G$. The mixing time in the uniform metric on $ G^\diamondsuit $ admits a sharp threshold, and equals $ |G|$ multiplied by the relaxation time on $G$, up to a factor of $ \log |G|$. For $ \mathbb {Z}_2 \wr \mathbb {Z}_n^2$, the lamplighter group over the discrete two dimensional torus, the relaxation time is of order $ n^2 \log n$, the total variation mixing time is of order $ n^2 \log^2 n$, and the uniform mixing time is of order $ n^4$. For $ \mathbb {Z}_2 \wr \mathbb {Z}_n^d$ when $ d \geq 3$, the relaxation time is of order $ n^d$, the total variation mixing time is of order $ n^d \log n$, and the uniform mixing time is of order $ n^{d + 2}$. In particular, these three quantities are of different orders of magnitude.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "cover time; lamplighter group; mixing time; random walks", } @Article{Lawler:2004:BEC, author = "Gregory Lawler and Vlada Limic", title = "The {Beurling} Estimate for a Class of Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "27:846--27:861", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-228", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/228", abstract = "An estimate of Beurling states that if $K$ is a curve from $0$ to the unit circle in the complex plane, then the probability that a Brownian motion starting at $ - \varepsilon $ reaches the unit circle without hitting the curve is bounded above by $ c \varepsilon^{1 / 2}$. This estimate is very useful in analysis of boundary behavior of conformal maps, especially for connected but rough boundaries. The corresponding estimate for simple random walk was first proved by Kesten. In this note we extend this estimate to random walks with zero mean, finite $ (3 + \delta)$-moment.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Beurling projection; escape probabilities; Green's function; random walk", } @Article{Puhalskii:2004:SDL, author = "Anatolii Puhalskii", title = "On Some Degenerate Large Deviation Problems", journal = j-ELECTRON-J-PROBAB, volume = "9", pages = "28:862--28:886", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v9-232", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/232", abstract = "This paper concerns the issue of obtaining the large deviation principle for solutions of stochastic equations with possibly degenerate coefficients. Specifically, we explore the potential of the methodology that consists in establishing exponential tightness and identifying the action functional via a maxingale problem. In the author's earlier work it has been demonstrated that certain convergence properties of the predictable characteristics of semimartingales ensure both that exponential tightness holds and that every large deviation accumulation point is a solution to a maxingale problem. The focus here is on the uniqueness for the maxingale problem. It is first shown that under certain continuity hypotheses existence and uniqueness of a solution to a maxingale problem of diffusion type are equivalent to Luzin weak existence and uniqueness, respectively, for the associated idempotent It{\^o} equation. Consequently, if the idempotent equation has a unique Luzin weak solution, then the action functional is specified uniquely, so the large deviation principle follows. Two kinds of application are considered. Firstly, we obtain results on the logarithmic asymptotics of moderate deviations for stochastic equations with possibly degenerate diffusion coefficients which, as compared with earlier results, relax the growth conditions on the coefficients, permit certain non-Lipshitz-continuous coefficients, and allow the coefficients to depend on the entire past of the process and to be discontinuous functions of time. The other application concerns multiple-server queues with impatient customers.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kim:2005:ESD, author = "Kyeong-Hun Kim", title = "{$ L_p $}-Estimates for {SPDE} with Discontinuous Coefficients in Domains", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "1:1--1:20", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-234", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/234", abstract = "Stochastic partial differential equations of divergence form with discontinuous and unbounded coefficients are considered in $ C^1 $ domains. Existence and uniqueness results are given in weighted $ L_p $ spaces, and Holder type estimates are presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic partial differential equations, discontinuous coefficients", } @Article{Newman:2005:CCN, author = "Charles Newman and Krishnamurthi Ravishankar and Rongfeng Sun", title = "Convergence of Coalescing Nonsimple Random Walks to the {Brownian Web}", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "2:21--2:60", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-235", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/235", abstract = "The Brownian Web (BW) is a family of coalescing Brownian motions starting from every point in space and time $ R \times R $. It was first introduced by Arratia, and later analyzed in detail by Toth and Werner. More recently, Fontes, Isopi, Newman and Ravishankar (FINR) gave a characterization of the BW, and general convergence criteria allowing in principle either crossing or noncrossing paths, which they verified for coalescing simple random walks. Later Ferrari, Fontes, and Wu verified these criteria for a two dimensional Poisson Tree. In both cases, the paths are noncrossing. To date, the general convergence criteria of FINR have not been verified for any case with crossing paths, which appears to be significantly more difficult than the noncrossing paths case. Accordingly, in this paper, we formulate new convergence criteria for the crossing paths case, and verify them for non-simple coalescing random walks satisfying a finite fifth moment condition. This is the first time that convergence to the BW has been proved for models with crossing paths. Several corollaries are presented, including an analysis of the scaling limit of voter model interfaces that extends a result of Cox and Durrett.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian Web, Invariance Principle, Coalescing Random Walks, Brownian Networks, Continuum Limit", } @Article{Kontoyiannis:2005:LDA, author = "Ioannis Kontoyiannis and Sean Meyn", title = "Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular {Markov} Processes", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "3:61--3:123", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-231", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/231", abstract = "In this paper we continue the investigation of the spectral theory and exponential asymptotics of primarily discrete-time Markov processes, following Kontoyiannis and Meyn (2003). We introduce a new family of nonlinear Lyapunov drift criteria, which characterize distinct subclasses of geometrically ergodic Markov processes in terms of simple inequalities for the nonlinear generator. We concentrate primarily on the class of multiplicatively regular Markov processes, which are characterized via simple conditions similar to (but weaker than) those of Donsker--Varadhan. For any such process $ \{ \Phi (t) \} $ with transition kernel $P$ on a general state space $X$, the following are obtained. Spectral Theory: For a large class of (possibly unbounded) functionals $F$ on $X$, the kernel $ \hat P(x, d y) = e^{F(x)} P(x, d y)$ has a discrete spectrum in an appropriately defined Banach space. It follows that there exists a ``maximal, '' well-behaved solution to the ``multiplicative Poisson equation, '' defined as an eigenvalue problem for $ \hat P$. Multiplicative Mean Ergodic Theorem: Consider the partial sums of this process with respect to any one of the functionals $F$ considered above. The normalized mean of their moment generating function (and not the logarithm of the mean) converges to the above maximal eigenfunction exponentially fast. Multiplicative regularity: The Lyapunov drift criterion under which our results are derived is equivalent to the existence of regeneration times with finite exponential moments for the above partial sums. Large Deviations: The sequence of empirical measures of the process satisfies a large deviations principle in a topology finer that the usual tau-topology, generated by the above class of functionals. The rate function of this LDP is the convex dual of logarithm of the above maximal eigenvalue, and it is shown to coincide with the Donsker--Varadhan rate function in terms of relative entropy. Exact Large Deviations Asymptotics: The above partial sums are shown to satisfy an exact large deviations expansion, analogous to that obtained by Bahadur and Ranga Rao for independent random variables.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov process, large deviations, entropy, Lyapunov function, empirical measures, nonlinear generator, large deviations principle", } @Article{Bass:2005:ASI, author = "Richard Bass and Jay Rosen", title = "An Almost Sure Invariance Principle for Renormalized Intersection Local Times", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "4:124--4:164", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-236", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/236", abstract = "Let $ \beta_k(n) $ be the number of self-intersections of order $k$, appropriately renormalized, for a mean zero planar random walk with $ 2 + \delta $ moments. On a suitable probability space we can construct the random walk and a planar Brownian motion $ W_t$ such that for each $ k \geq 2$, $ | \beta_k(n) - \gamma_k(n)| = o(1)$, a.s., where $ \gamma_k(n)$ is the renormalized self-intersection local time of order $k$ at time 1 for the Brownian motion $ W_{nt} / \sqrt n$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Schuhmacher:2005:DEP, author = "Dominic Schuhmacher", title = "Distance Estimates for {Poisson} Process Approximations of Dependent Thinnings", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "5:165--5:201", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-237", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/237", abstract = "It is well known, that under certain conditions, gradual thinning of a point process on $ R^d_+ $, accompanied by a contraction of space to compensate for the thinning, leads in the weak limit to a Cox process. In this article, we apply discretization and a result based on Stein's method to give estimates of the Barbour--Brown distance $ d_2 $ between the distribution of a thinned point process and an approximating Poisson process, and evaluate the estimates in concrete examples. We work in terms of two, somewhat different, thinning models. The main model is based on the usual thinning notion of deleting points independently according to probabilities supplied by a random field. In Section 4, however, we use an alternative thinning model, which can be more straightforward to apply if the thinning is determined by point interactions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Eisenbaum:2005:CBG, author = "Nathalie Eisenbaum", title = "A Connection between {Gaussian} Processes and {Markov} Processes", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "6:202--6:215", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-238", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/238", abstract = "The Green function of a transient symmetric Markov process can be interpreted as the covariance of a centered Gaussian process. This relation leads to several fruitful identities in law. Symmetric Markov processes and their associated Gaussian process both benefit from these connections. Therefore it is of interest to characterize the associated Gaussian processes. We present here an answer to that question.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Cancrini:2005:DLT, author = "Nicoletta Cancrini and Filippo Cesi and Cyril Roberto", title = "Diffusive Long-time Behavior of {Kawasaki} Dynamics", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "7:216--7:249", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-239", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/239", abstract = "If $ P_t $ is the semigroup associated with the Kawasaki dynamics on $ Z^d $ and $f$ is a local function on the configuration space, then the variance with respect to the invariant measure $ \mu $ of $ P_t f$ goes to zero as $ t \to \infty $ faster than $ t^{-d / 2 + \varepsilon }$, with $ \varepsilon $ arbitrarily small. The fundamental assumption is a mixing condition on the interaction of Dobrushin and Schlosman type.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Heicklen:2005:RPS, author = "Deborah Heicklen and Christopher Hoffman", title = "Return Probabilities of a Simple Random Walk on Percolation Clusters", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "8:250--8:302", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-240", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/240", abstract = "We bound the probability that a continuous time simple random walk on the infinite percolation cluster on $ Z^d $ returns to the origin at time $t$. We use this result to show that in dimensions 5 and higher the uniform spanning forest on infinite percolation clusters supported on graphs with infinitely many connected components a.s.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Birkner:2005:ASB, author = "Matthias Birkner and Jochen Blath and Marcella Capaldo and Alison Etheridge and Martin M{\"o}hle and Jason Schweinsberg and Anton Wakolbinger", title = "Alpha-Stable Branching and Beta-Coalescents", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "9:303--9:325", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-241", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/241", abstract = "We determine that the continuous-state branching processes for which the genealogy, suitably time-changed, can be described by an autonomous Markov process are precisely those arising from $ \alpha $-stable branching mechanisms. The random ancestral partition is then a time-changed $ \Lambda $-coalescent, where $ \Lambda $ is the Beta-distribution with parameters $ 2 - \alpha $ and $ \alpha $, and the time change is given by $ Z^{1 - \alpha }$, where $Z$ is the total population size. For $ \alpha = 2$ (Feller's branching diffusion) and $ \Lambda = \delta_0$ (Kingman's coalescent), this is in the spirit of (a non-spatial version of) Perkins' Disintegration Theorem. For $ \alpha = 1$ and $ \Lambda $ the uniform distribution on $ [0, 1]$, this is the duality discovered by Bertoin \& Le Gall (2000) between the norming of Neveu's continuous state branching process and the Bolthausen--Sznitman coalescent.\par We present two approaches: one, exploiting the `modified lookdown construction', draws heavily on Donnelly \& Kurtz (1999); the other is based on direct calculations with generators.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Berzin:2005:CFM, author = "Corinne Berzin and Jos{\'e} Le{\'o}n", title = "Convergence in Fractional Models and Applications", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "10:326--10:370", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-172", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/172", abstract = "We consider a fractional Brownian motion with Hurst parameter strictly between 0 and 1. We are interested in the asymptotic behaviour of functionals of the increments of this and related processes and we propose several probabilistic and statistical applications.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractional Brownian motion; Level crossings; limit theorem; local time; rate of convergence", } @Article{Salminen:2005:PIF, author = "Paavo Salminen and Marc Yor", title = "Perpetual Integral Functionals as Hitting and Occupation Times", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "11:371--11:419", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-256", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/256", abstract = "Let $X$ be a linear diffusion and $f$ a non-negative, Borel measurable function. We are interested in finding conditions on $X$ and $f$ which imply that the perpetual integral functional\par $$ I^X_\infty (f) := \int_0^\infty f(X_t) d t $$ is identical in law with the first hitting time of a point for some other diffusion. This phenomenon may often be explained using random time change. Because of some potential applications in mathematical finance, we are considering mainly the case when $X$ is a Brownian motion with drift $ \mu > 0, $ denoted $ {B^{(\mu)}_t \colon t \geq 0}, $ but it is obvious that the method presented is more general. We also review the known examples and give new ones. In particular, results concerning one-sided functionals\par $$ \int_0^\infty f(B^{(\mu)}_t){\bf 1}_{{B^{(\mu)}_t < 0}} d t \quad {\rm and} \quad \int_0^\infty f(B^{(\mu)}_t){\bf 1}_{{B^{(\mu)}_t > 0}} d t $$ are presented. This approach generalizes the proof, based on the random time change techniques, of the fact that the Dufresne functional (this corresponds to $ f(x) = \exp ( - 2 x)), $ playing quite an important role in the study of geometric Brownian motion, is identical in law with the first hitting time for a Bessel process. Another functional arising naturally in this context is\par $$ \int_0^\infty \big (a + \exp (B^{(\mu)}_t) \big)^{-2} d t, $$ which is seen, in the case $ \mu = 1 / 2, $ to be identical in law with the first hitting time for a Brownian motion with drift $ \mu = a / 2.$ The paper is concluded by discussing how the Feynman--Kac formula can be used to find the distribution of a perpetual integral functional.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chauvin:2005:MPB, author = "B. Chauvin and T. Klein and J.-F. Marckert and A. Rouault", title = "Martingales and Profile of Binary Search Trees", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "12:420--12:435", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-257", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/257", abstract = "We are interested in the asymptotic analysis of the binary search tree (BST) under the random permutation model. Via an embedding in a continuous time model, we get new results, in particular the asymptotic behavior of the profile.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Mountford:2005:TCN, author = "Thomas Mountford and Li-Chau Wu", title = "The Time for a Critical Nearest Particle System to reach Equilibrium starting with a large Gap", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "13:436--13:498", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-242", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/242", abstract = "We consider the time for a critical nearest particle system, starting in equilibrium subject to possessing a large gap, to achieve equilibrium.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Interacting Particle Systems, Reversibility, Convergence to equilibrium", } @Article{Panchenko:2005:CLT, author = "Dmitry Panchenko", title = "A {Central Limit Theorem} for Weighted Averages of Spins in the High Temperature Region of the {Sherrington--Kirkpatrick} Model", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "14:499--14:524", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-258", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/258", abstract = "In this paper we prove that in the high temperature region of the Sherrington--Kirkpatrick model for a typical realization of the disorder the weighted average of spins $ \sum_{i \leq N} t_i \sigma_i $ will be approximately Gaussian provided that $ \max_{i \leq N}|t_i| / \sum_{i \leq N} t_i^2 $ is small.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{DaiPra:2005:LSI, author = "Paolo {Dai Pra} and Gustavo Posta", title = "Logarithmic {Sobolev} Inequality for Zero--Range Dynamics: Independence of the Number of Particles", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "15:525--15:576", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-259", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/259", abstract = "We prove that the logarithmic-Sobolev constant for Zero-Range Processes in a box of diameter $L$ may depend on $L$ but not on the number of particles. This is a first, but relevant and quite technical step, in the proof that this logarithmic-Sobolev constant grows as the square of $L$, that is presented in a forthcoming paper.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chen:2005:LDL, author = "Xia Chen and Wenbo Li and Jay Rosen", title = "Large Deviations for Local Times of Stable Processes and Stable Random Walks in 1 Dimension", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "16:577--16:608", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-260", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/260", abstract = "In Chen and Li (2004), large deviations were obtained for the spatial $ L^p $ norms of products of independent Brownian local times and local times of random walks with finite second moment. The methods of that paper depended heavily on the continuity of the Brownian path and the fact that the generator of Brownian motion, the Laplacian, is a local operator. In this paper we generalize these results to local times of symmetric stable processes and stable random walks.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Biggins:2005:FPS, author = "John Biggins and Andreas Kyprianou", title = "Fixed Points of the Smoothing Transform: the Boundary Case", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "17:609--17:631", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-255", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/255", abstract = "Let $ A = (A_1, A_2, A_3, \ldots) $ be a random sequence of non-negative numbers that are ultimately zero with $ E[\sum A_i] = 1 $ and $ E \left [\sum A_i \log A_i \right] \leq 0 $. The uniqueness of the non-negative fixed points of the associated smoothing transform is considered. These fixed points are solutions to the functional equation $ \Phi (\psi) = E \left [\prod_i \Phi (\psi A_i) \right], $ where $ \Phi $ is the Laplace transform of a non-negative random variable. The study complements, and extends, existing results on the case when $ E \left [\sum A_i \log A_i \right] < 0 $. New results on the asymptotic behaviour of the solutions near zero in the boundary case, where $ E \left [\sum A_i \log A_i \right] = 0 $, are obtained.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching random walk; functional equation; Smoothing transform", } @Article{Cabanal-Duvillard:2005:MRB, author = "Thierry Cabanal-Duvillard", title = "A Matrix Representation of the {Bercovici--Pata} Bijection", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "18:632--18:661", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-246", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/246", abstract = "Let $ \mu $ be an infinitely divisible law on the real line, $ \Lambda (\mu) $ its freely infinitely divisible image by the Bercovici--Pata bijection. The purpose of this article is to produce a new kind of random matrices with distribution $ \mu $ at dimension 1, and with its empirical spectral law converging to $ \Lambda (\mu) $ as the dimension tends to infinity. This constitutes a generalisation of Wigner's result for the Gaussian Unitary Ensemble.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random matrices, free probability, infinitely divisible laws", } @Article{Lozada-Chang:2005:LDM, author = "Li-Vang Lozada-Chang", title = "Large Deviations on Moment Spaces", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "19:662--19:690", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-202", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/202", abstract = "In this paper we study asymptotic behavior of some moment spaces. We consider two different settings. In the first one, we work with ordinary multi-dimensional moments on the standard $m$-simplex. In the second one, we deal with the trigonometric moments on the unit circle of the complex plane. We state large and moderate deviation principles for uniformly distributed moments. In both cases the rate function of the large deviation principle is related to the reversed Kullback information with respect to the uniform measure on the integration space.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "large deviations; multidimensional moment; random moment problem", } @Article{Begyn:2005:QVA, author = "Arnaud Begyn", title = "Quadratic Variations along Irregular Subdivisions for {Gaussian} Processes", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "20:691--20:717", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-245", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/245", abstract = "In this paper we deal with second order quadratic variations along general subdivisions for processes with Gaussian increments. These have almost surely a deterministic limit under conditions on the mesh of the subdivisions. This limit depends on the singularity function of the process and on the structure of the subdivisions too. Then we illustrate the results with the example of the time-space deformed fractional Brownian motion and we present some simulations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "estimation, fractional processes, Gaussian processes, generalized quadratic variations, irregular subdivisions, singularity function", } @Article{Goldschmidt:2005:RRT, author = "Christina Goldschmidt and James Martin", title = "Random Recursive Trees and the {Bolthausen--Sznitman} Coalesent", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "21:718--21:745", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-265", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/265", abstract = "We describe a representation of the Bolthausen--Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the coalescent restricted to $ [n] $: we show that the distribution of the number of blocks involved in the final collision converges as $ n \to \infty $, and obtain a scaling law for the sizes of these blocks. We also consider the discrete-time Markov chain giving the number of blocks after each collision of the coalescent restricted to $ [n] $; we show that the transition probabilities of the time-reversal of this Markov chain have limits as $ n \to \infty $. These results can be interpreted as describing a ``post-gelation'' phase of the Bolthausen--Sznitman coalescent, in which a giant cluster containing almost all of the mass has already formed and the remaining small blocks are being absorbed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bouchard:2005:HAO, author = "Bruno Bouchard and Emmanuel Teman", title = "On the Hedging of {American} Options in Discrete Time with Proportional Transaction Costs", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "22:746--22:760", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-266", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/266", abstract = "In this note, we consider a general discrete time financial market with proportional transaction costs as in Kabanov and Stricker (2001), Kabanov et al. (2002), Kabanov et al. (2003) and Schachermayer (2004). We provide a dual formulation for the set of initial endowments which allow to super-hedge some American claim. We show that this extends the result of Chalasani and Jha (2001) which was obtained in a model with constant transaction costs and risky assets which evolve on a finite dimensional tree. We also provide fairly general conditions under which the expected formulation in terms of stopping times does not work.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Coutin:2005:SMR, author = "Laure Coutin and Antoine Lejay", title = "Semi-martingales and rough paths theory", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "23:761--23:785", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-162", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/162", abstract = "We prove that the theory of rough paths, which is used to define path-wise integrals and path-wise differential equations, can be used with continuous semi-martingales. We provide then an almost sure theorem of type Wong--Zakai. Moreover, we show that the conditions UT and UCV, used to prove that one can interchange limits and It{\^o} or Stratonovich integrals, provide the same result when one uses the rough paths theory.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$p$-variation; conditions UT and UCV; iterated integrals; rough paths; Semi-martingales; Wong--Zakai theorem", } @Article{Cassandro:2005:ODR, author = "Marzio Cassandro and Enza Orlandi and Pierre Picco and Maria Eulalia Vares", title = "One-dimensional Random Field {Kac}'s Model: Localization of the Phases", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "24:786--24:864", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-263", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/263", abstract = "We study the typical profiles of a one dimensional random field Kac model, for values of the temperature and magnitude of the field in the region of two absolute minima for the free energy of the corresponding random field Curie Weiss model. We show that, for a set of realizations of the random field of overwhelming probability, the localization of the two phases corresponding to the previous minima is completely determined. Namely, we are able to construct random intervals tagged with a sign, where typically, with respect to the infinite volume Gibbs measure, the profile is rigid and takes, according to the sign, one of the two values corresponding to the previous minima. Moreover, we characterize the transition from one phase to the other. The analysis extends the one done by Cassandro, Orlandi and Picco in [13].", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Phase transition, random walk, random environment, Kac potential", } @Article{Flandoli:2005:SVF, author = "Franco Flandoli and Massimiliano Gubinelli", title = "Statistics of a Vortex Filament Model", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "25:865--25:900", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-267", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/267", abstract = "A random incompressible velocity field in three dimensions composed by Poisson distributed Brownian vortex filaments is constructed. The filaments have a random thickness, length and intensity, governed by a measure $ \gamma $. Under appropriate assumptions on $ \gamma $ we compute the scaling law of the structure function of the field and show that, in particular, it allows for either K41-like scaling or multifractal scaling.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Fulman:2005:SMD, author = "Jason Fulman", title = "{Stein}'s Method and Descents after Riffle Shuffles", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "26:901--26:924", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-268", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/268", abstract = "Berestycki and Durrett used techniques from random graph theory to prove that the distance to the identity after iterating the random transposition shuffle undergoes a transition from Poisson to normal behavior. This paper establishes an analogous result for distance after iterates of riffle shuffles or iterates of riffle shuffles and cuts. The analysis uses different tools: Stein's method and generating functions. A useful technique which emerges is that of making a problem more tractable by adding extra symmetry, then using Stein's method to exploit the symmetry in the modified problem, and from this deducing information about the original problem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Csaki:2005:IPV, author = "Endre Csaki and Yueyun Hu", title = "On the Increments of the Principal Value of {Brownian} Local Time", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "27:925--27:947", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-269", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/269", abstract = "Let $W$ be a one-dimensional Brownian motion starting from 0. Define $ Y(t) = \int_0^t{ds \over W(s)} := \lim_{\epsilon \to 0} \int_0^t 1_{(|W(s)| > \epsilon)} {ds \over W(s)}$ as Cauchy's principal value related to local time. We prove limsup and liminf results for the increments of $Y$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chaumont:2005:LPC, author = "Lo{\"\i}c Chaumont and Ronald Doney", title = "On {L{\'e}vy} processes conditioned to stay positive", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "28:948--28:961", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-261", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See corrections \cite{Chaumont:2008:CLP}.", URL = "http://ejp.ejpecp.org/article/view/261", abstract = "We construct the law of L{\'e}vy processes conditioned to stay positive under general hypotheses. We obtain a Williams type path decomposition at the minimum of these processes. This result is then applied to prove the weak convergence of the law of L{\'e}vy processes conditioned to stay positive as their initial state tends to 0. We describe an absolute continuity relationship between the limit law and the measure of the excursions away from 0 of the underlying L{\'e}vy process reflected at its minimum. Then, when the L{\'e}vy process creeps upwards, we study the lower tail at 0 of the law of the height of this excursion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "L'evy process conditioned to stay positive, path decomposition, weak convergence, excursion measure, creeping", } @Article{Posta:2005:EFO, author = "Gustavo Posta", title = "Equilibrium Fluctuations for a One-Dimensional Interface in the Solid on Solid Approximation", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "29:962--29:987", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-270", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/270", abstract = "An unbounded one-dimensional solid-on-solid model with integer heights is studied. Unbounded here means that there is no {\em a priori} restrictions on the discrete gradient of the interface. The interaction Hamiltonian of the interface is given by a finite range part, proportional to the sum of height differences, plus a part of exponentially decaying long range potentials. The evolution of the interface is a reversible Markov process. We prove that if this system is started in the center of a box of size $L$ after a time of order $ L^3$ it reaches, with a very large probability, the top or the bottom of the box.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bahlali:2005:GSM, author = "Seid Bahlali and Brahim Mezerdi", title = "A General Stochastic Maximum Principle for Singular Control Problems", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "30:988--30:1004", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-271", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/271", abstract = "We consider the stochastic control problem in which the control domain need not be convex, the control variable has two components, the first being absolutely continuous and the second singular. The coefficients of the state equation are non linear and depend explicitly on the absolutely continuous component of the control. We establish a maximum principle, by using a spike variation on the absolutely continuous part of the control and a convex perturbation on the singular one. This result is a generalization of Peng's maximum principle to singular control problems.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chorro:2005:CDL, author = "Christophe Chorro", title = "Convergence in {Dirichlet} Law of Certain Stochastic Integrals", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "31:1005--31:1025", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-272", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/272", abstract = "Recently, Nicolas Bouleau has proposed an extension of the Donsker's invariance principle in the framework of Dirichlet forms. He proves that an erroneous random walk of i.i.d random variables converges in Dirichlet law toward the Ornstein--Uhlenbeck error structure on the Wiener space. The aim of this paper is to extend this result to some families of stochastic integrals.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ganesh:2005:SPL, author = "Ayalvadi Ganesh and Claudio Macci and Giovanni Torrisi", title = "Sample Path Large Deviations Principles for {Poisson} Shot Noise Processes and Applications", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "32:1026--32:1043", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-273", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/273", abstract = "This paper concerns sample path large deviations for Poisson shot noise processes, and applications in queueing theory. We first show that, under an exponential tail condition, Poisson shot noise processes satisfy a sample path large deviations principle with respect to the topology of pointwise convergence. Under a stronger superexponential tail condition, we extend this result to the topology of uniform convergence. We also give applications of this result to determining the most likely path to overflow in a single server queue, and to finding tail asymptotics for the queue lengths at priority queues.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "large deviations; Poisson shot noise; queues; risk; sample paths", } @Article{Bell:2005:DSP, author = "Steven Bell and Ruth Williams", title = "Dynamic Scheduling of a Parallel Server System in Heavy Traffic with Complete Resource Pooling: Asymptotic Optimality of a Threshold Policy", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "33:1044--33:1115", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-281", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/281", abstract = "We consider a parallel server queueing system consisting of a bank of buffers for holding incoming jobs and a bank of flexible servers for processing these jobs. Incoming jobs are classified into one of several different classes (or buffers). Jobs within a class are processed on a first-in-first-out basis, where the processing of a given job may be performed by any server from a given (class-dependent) subset of the bank of servers. The random service time of a job may depend on both its class and the server providing the service. Each job departs the system after receiving service from one server. The system manager seeks to minimize holding costs by dynamically scheduling waiting jobs to available servers. We consider a parameter regime in which the system satisfies both a heavy traffic and a complete resource pooling condition. Our cost function is an expected cumulative discounted cost of holding jobs in the system, where the (undiscounted) cost per unit time is a linear function of normalized (with heavy traffic scaling) queue length. In a prior work, the second author proposed a continuous review threshold control policy for use in such a parallel server system. This policy was advanced as an ``interpretation'' of the analytic solution to an associated Brownian control problem (formal heavy traffic diffusion approximation). In this paper we show that the policy proposed previously is asymptotically optimal in the heavy traffic limit and that the limiting cost is the same as the optimal cost in the Brownian control problem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ledoux:2005:DIE, author = "Michel Ledoux", title = "Distributions of Invariant Ensembles from the Classical Orthogonal Polynimials: the Discrete Case", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "34:1116--34:1146", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-282", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/282", abstract = "We examine the Charlier, Meixner, Krawtchouk and Hahn discrete orthogonal polynomial ensembles, deeply investigated by K. Johansson, using integration by parts for the underlying Markov operators, differential equations on Laplace transforms and moment equations. As for the matrix ensembles, equilibrium measures are described as limits of empirical spectral distributions. In particular, a new description of the equilibrium measures as adapted mixtures of the universal arcsine law with an independent uniform distribution is emphasized. Factorial moment identities on mean spectral measures may be used towards small deviation inequalities on the rightmost charges at the rate given by the Tracy--Widom asymptotics.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Durrett:2005:CSB, author = "Richard Durrett and Leonid Mytnik and Edwin Perkins", title = "Competing super-{Brownian} motions as limits of interacting particle systems", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "35:1147--35:1220", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-229", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/229", abstract = "We study two-type branching random walks in which the birth or death rate of each type can depend on the number of neighbors of the opposite type. This competing species model contains variants of Durrett's predator-prey model and Durrett and Levin's colicin model as special cases. We verify in some cases convergence of scaling limits of these models to a pair of super-Brownian motions interacting through their collision local times, constructed by Evans and Perkins.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "super-Brownian motion, interacting branching particle systems, collision local time, competing species, measure-valued diffusions", } @Article{Sethuraman:2005:MPD, author = "Sunder Sethuraman and Srinivasa Varadhan", title = "A Martingale Proof of {Dobrushin}'s Theorem for Non-Homogeneous {Markov} Chains", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "36:1221--36:1235", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-283", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/283", abstract = "In 1956, Dobrushin proved an important central limit theorem for non-homogeneous Markov chains. In this note, a shorter and different proof elucidating more the assumptions is given through martingale approximation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ariyoshi:2005:STA, author = "Teppei Ariyoshi and Masanori Hino", title = "Small-time Asymptotic Estimates in Local {Dirichlet} Spaces", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "37:1236--37:1259", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-286", ISSN = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/286", abstract = "Small-time asymptotic estimates of semigroups on a logarithmic scale are proved for all symmetric local Dirichlet forms on $ \sigma $-finite measure spaces, which is an extension of the work by Hino and Ram{\'\i}rez [4].", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Wang:2005:LTS, author = "Qiying Wang", title = "Limit Theorems for Self-Normalized Large Deviation", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "38:1260--38:1285", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-289", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/289", abstract = "Let $ X, X_1, X_2, \cdots $ be i.i.d. random variables with zero mean and finite variance $ \sigma^2 $. It is well known that a finite exponential moment assumption is necessary to study limit theorems for large deviation for the standardized partial sums. In this paper, limit theorems for large deviation for self-normalized sums are derived only under finite moment conditions. In particular, we show that, if $ E X^4 < \infty $, then \par $$ \frac {P(S_n / V_n \geq x)}{1 - \Phi (x)} = \exp \left \{ - \frac {x^3 EX^3}{3 \sqrt { n} \sigma^3} \right \} \left [1 + O \left (\frac {1 + x}{\sqrt { n}} \right) \right], $$ for $ x \ge 0 $ and $ x = O(n^{1 / 6}) $, where $ S_n = \sum_{i = 1}^n X_i $ and $ V_n = (\sum_{i = 1}^n X_i^2)^{1 / 2} $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cram{\'e}r large deviation, limit theorem", } @Article{Greven:2005:RTI, author = "Andreas Greven and Vlada Limic and Anita Winter", title = "Representation Theorems for Interacting {Moran} Models, Interacting {Fisher--Wrighter} Diffusions and Applications", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "39:1286--39:1358", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-290", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/290", abstract = "We consider spatially interacting Moran models and their diffusion limit which are interacting Fisher--Wright diffusions. The Moran model is a spatial population model with individuals of different type located on sites given by elements of an Abelian group. The dynamics of the system consists of independent migration of individuals between the sites and a resampling mechanism at each site, i.e., pairs of individuals are replaced by new pairs where each newcomer takes the type of a randomly chosen individual from the parent pair. Interacting Fisher--Wright diffusions collect the relative frequency of a subset of types evaluated for the separate sites in the limit of infinitely many individuals per site. One is interested in the type configuration as well as the time-space evolution of genealogies, encoded in the so-called historical process. The first goal of the paper is the analytical characterization of the historical processes for both models as solutions of well-posed martingale problems and the development of a corresponding duality theory. For that purpose, we link both the historical Fisher--Wright diffusions and the historical Moran models by the so-called look-down process. That is, for any fixed time, a collection of historical Moran models with increasing particle intensity and a particle representation for the limiting historical interacting Fisher--Wright diffusions are provided on one and the same probability space. This leads to a strong form of duality between spatially interacting Moran models, interacting Fisher--Wright diffusions on the one hand and coalescing random walks on the other hand, which extends the classical weak form of moment duality for interacting Fisher--Wright diffusions. Our second goal is to show that this representation can be used to obtain new results on the long-time behavior, in particular (i) on the structure of the equilibria, and of the equilibrium historical processes, and (ii) on the behavior of our models on large but finite site space in comparison with our models on infinite site space. Here the so-called finite system scheme is established for spatially interacting Moran models which implies via the look-down representation also the already known results for interacting Fisher--Wright diffusions. Furthermore suitable versions of the finite system scheme on the level of historical processes are newly developed and verified. In the long run the provided look-down representation is intended to answer questions about finer path properties of interacting Fisher--Wright diffusions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "equilibrium measure; exchangeability; historical martingale problem; historical process; Interacting Fischer--Wright diffusions; large finite systems; look-down construction; spatially interacting Moran model", } @Article{Puchala:2005:EAT, author = "Zbigniew Puchala and Tomasz Rolski", title = "The Exact Asymptotic of the Time to Collision", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "40:1359--40:1380", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-291", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/291", abstract = "In this note we consider the time of the collision $ \tau $ for $n$ independent copies of Markov processes $ X^1_t, \ldots {}, X^n_t$, each starting from $ x_i$, where $ x_1 < \ldots {} < x_n$. We show that for the continuous time random walk $ P_x(\tau > t) = t^{-n(n - 1) / 4}(C h(x) + o(1)), $ where $C$ is known and $ h(x)$ is the Vandermonde determinant. From the proof one can see that the result also holds for $ X_t$ being the Brownian motion or the Poisson process. An application to skew standard Young tableaux is given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; collision time; continuous time random walk; skew Young tableaux; tandem queue", } @Article{Igloi:2005:ROT, author = "Endre Igl{\'o}i", title = "A Rate-Optimal Trigonometric Series Expansion of the Fractional {Brownian} Motion", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "41:1381--41:1397", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-287", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/287", abstract = "Let $ B^{(H)}(t), t \in \lbrack - 1, 1] $, be the fractional Brownian motion with Hurst parameter $ H \in (1 / 2, 1) $. In this paper we present the series representation $ B^{(H)}(t) = a_0 t \xi_0 + \sum_{j = 1}^{\infty }a_j((1 - \cos (j \pi t)) \xi_j + \sin (j \pi t) \widetilde {\xi }_j), t \in \lbrack - 1, 1] $, where $ a_j, j \in \mathbb {N} \cup {0} $, are constants given explicitly, and $ \xi_j, j \in \mathbb {N} \cup {0} $, $ \widetilde {\xi }_j, j \in \mathbb {N} $, are independent standard Gaussian random variables. We show that the series converges almost surely in $ C[ - 1, 1] $, and in mean-square (in $ L^2 (\Omega)$), uniformly in $ t \in \lbrack - 1, 1]$. Moreover we prove that the series expansion has an optimal rate of convergence.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractional Brownian motion; function series expansion; Gamma-mixed Ornstein--Uhlenbeck process; rate of convergence", } @Article{Mikulevicius:2005:CDP, author = "Remigijus Mikulevicius and Henrikas Pragarauskas", title = "On {Cauchy--Dirichlet} Problem in Half-Space for Linear Integro-Differential Equations in Weighted {H{\"o}lder} Spaces", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "42:1398--42:1416", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-292", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/292", abstract = "We study the Cauchy--Dirichlet problem in half-space for linear parabolic integro-differential equations. Sufficient conditions are derived under which the problem has a unique solution in weighted Hoelder classes. The result can be used in the regularity analysis of certain functionals arising in the theory of Markov processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov jump processes, parabolic integro-differential equations", } @Article{Jean:2005:RWG, author = "Mairesse Jean", title = "Random Walks on Groups and Monoids with a {Markovian} Harmonic Measure", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "43:1417--43:1441", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-293", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/293", abstract = "We consider a transient nearest neighbor random walk on a group $G$ with finite set of generators $S$. The pair $ (G, S)$ is assumed to admit a natural notion of normal form words where only the last letter is modified by multiplication by a generator. The basic examples are the free products of a finitely generated free group and a finite family of finite groups, with natural generators. We prove that the harmonic measure is Markovian of a particular type. The transition matrix is entirely determined by the initial distribution which is itself the unique solution of a finite set of polynomial equations of degree two. This enables to efficiently compute the drift, the entropy, the probability of ever hitting an element, and the minimal positive harmonic functions of the walk. The results extend to monoids.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Finitely generated group or monoid; free product; harmonic measure.; random walk", } @Article{Kozdron:2005:ERW, author = "Michael Kozdron and Gregory Lawler", title = "Estimates of Random Walk Exit Probabilities and Application to Loop-Erased Random Walk", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "44:1442--44:1467", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-294", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/294", abstract = "We prove an estimate for the probability that a simple random walk in a simply connected subset $A$ of $ Z^2$ starting on the boundary exits $A$ at another specified boundary point. The estimates are uniform over all domains of a given inradius. We apply these estimates to prove a conjecture of S. Fomin in 2001 concerning a relationship between crossing probabilities of loop-erased random walk and Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Cvitanic:2005:SDM, author = "Jaksa Cvitanic and Jianfeng Zhang", title = "The Steepest Descent Method for Forward--Backward {SDEs}", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "45:1468--45:1495", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-295", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/295", abstract = "This paper aims to open a door to Monte-Carlo methods for numerically solving Forward--Backward SDEs, without computing over all Cartesian grids as usually done in the literature. We transform the FBSDE to a control problem and propose the steepest descent method to solve the latter one. We show that the original (coupled) FBSDE can be approximated by {it decoupled} FBSDEs, which further comes down to computing a sequence of conditional expectations. The rate of convergence is obtained, and the key to its proof is a new well-posedness result for FBSDEs. However, the approximating decoupled FBSDEs are non-Markovian. Some Markovian type of modification is needed in order to make the algorithm efficiently implementable.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hausenblas:2005:EUR, author = "Erika Hausenblas", title = "Existence, Uniqueness and Regularity of Parabolic {SPDEs} Driven by {Poisson} Random Measure", journal = j-ELECTRON-J-PROBAB, volume = "10", pages = "46:1496--46:1546", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v10-297", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/297", abstract = "In this paper we investigate SPDEs in certain Banach spaces driven by a Poisson random measure. We show existence and uniqueness of the solution, investigate certain integrability properties and verify the c{\`a}dl{\`a}g property.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Goel:2006:MTB, author = "Sharad Goel and Ravi Montenegro and Prasad Tetali", title = "Mixing Time Bounds via the Spectral Profile", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "1:1--1:26", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-300", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/300", abstract = "On complete, non-compact manifolds and infinite graphs, Faber--Krahn inequalities have been used to estimate the rate of decay of the heat kernel. We develop this technique in the setting of finite Markov chains, proving upper and lower $ L^{\infty } $ mixing time bounds via the spectral profile. This approach lets us recover and refine previous conductance-based bounds of mixing time (including the Morris--Peres result), and in general leads to sharper estimates of convergence rates. We apply this method to several models including groups with moderate growth, the fractal-like Viscek graphs, and the product group $ Z_a \times Z_b $, to obtain tight bounds on the corresponding mixing times.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Alsmeyer:2006:SFP, author = "Gerold Alsmeyer and Uwe R{\"o}sler", title = "A Stochastic Fixed Point Equation Related to Weighted Branching with Deterministic Weights", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "2:27--2:56", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-296", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/296", abstract = "For real numbers $ C, T_1, T_2, \ldots {} $ we find all solutions $ \mu $ to the stochastic fixed point equation $ W \sim \sum_{j \ge 1}T_j W_j + C $, where $ W, W_1, W_2, \ldots {} $ are independent real-valued random variables with distribution $ \mu $ and $ \sim $ means equality in distribution. All solutions are infinitely divisible. The set of solutions depends on the closed multiplicative subgroup of $ { R}_*= { R} \backslash \{ 0 \} $ generated by the $ T_j $. If this group is continuous, i.e., $ {R}_* $ itself or the positive half line $ {R}_+ $, then all nontrivial fixed points are stable laws. In the remaining (discrete) cases further periodic solutions arise. A key observation is that the Levy measure of any fixed point is harmonic with respect to $ \Lambda = \sum_{j \ge 1} \delta_{T_j} $, i.e., $ \Gamma = \Gamma \star \Lambda $, where $ \star $ means multiplicative convolution. This will enable us to apply the powerful Choquet--Deny theorem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Choquet--Deny theorem; infinite divisibility; L'evy measure; stable distribution; Stochastic fixed point equation; weighted branching process", } @Article{Cheridito:2006:DMR, author = "Patrick Cheridito and Freddy Delbaen and Michael Kupper", title = "Dynamic Monetary Risk Measures for Bounded Discrete-Time Processes", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "3:57--3:106", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-302", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/302", abstract = "We study dynamic monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a dynamic risk measure time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time. We show that this condition translates into a decomposition property for the corresponding acceptance sets, and we demonstrate how time-consistent dynamic monetary risk measures can be constructed by pasting together one-period risk measures. For conditional coherent and convex monetary risk measures, we provide dual representations of Legendre--Fenchel type based on linear functionals induced by adapted increasing processes of integrable variation. Then we give dual characterizations of time-consistency for dynamic coherent and convex monetary risk measures. To this end, we introduce a concatenation operation for adapted increasing processes of integrable variation, which generalizes the pasting of probability measures. In the coherent case, time-consistency corresponds to stability under concatenation in the dual. For dynamic convex monetary risk measures, the dual characterization of time-consistency generalizes to a condition on the family of convex conjugates of the conditional risk measures at different times. The theoretical results are applied by discussing the time-consistency of various specific examples of dynamic monetary risk measures that depend on bounded discrete-time processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Tang:2006:IND, author = "Qihe Tang", title = "Insensitivity to Negative Dependence of the Asymptotic Behavior of Precise Large Deviations", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "4:107--4:120", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-304", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/304", abstract = "Since the pioneering works of C. C. Heyde, A. V. Nagaev, and S. V. Nagaev in 1960's and 1970's, the precise asymptotic behavior of large-deviation probabilities of sums of heavy-tailed random variables has been extensively investigated by many people, but mostly it is assumed that the random variables under discussion are independent. In this paper, we extend the study to the case of negatively dependent random variables and we find out that the asymptotic behavior of precise large deviations is insensitive to the negative dependence.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "(lower/upper) negative dependence; (upper) Matuszewska index; Consistent variation; partial sum; precise large deviations; uniform asymptotics", } @Article{Hamadene:2006:BTR, author = "Said Hamadene and Mohammed Hassani", title = "{BSDEs} with two reflecting barriers driven by a {Brownian} motion and {Poisson} noise and related {Dynkin} game", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "5:121--5:145", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-303", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/303", abstract = "In this paper we study BSDEs with two reflecting barriers driven by a Brownian motion and an independent Poisson process. We show the existence and uniqueness of {\em local\/} and global solutions. As an application we solve the related zero-sum Dynkin game.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Backward stochastic differential equation; Dynkin game; Mokobodzki's condition; Poisson measure", } @Article{Song:2006:TSE, author = "Renming Song", title = "Two-sided Estimates on the Density of the {Feynman--Kac} Semigroups of Stable-like Processes", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "6:146--6:161", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-308", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/308", abstract = "In this paper we establish two-sided estimates for the density of the Feynman--Kac semigroups of stable-like processes with potentials given by signed measures belonging to the Kato class. We also provide similar estimates for the densities of two other kinds of Feynman--Kac semigroups of stable-like processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "continuous additive functionals; continuous additive functionals of zero energy; Feynman--Kac semigroups; Kato class; purely discontinuous additive functionals.; Stable processes; stable-like processes", } @Article{Tsirelson:2006:BLM, author = "Boris Tsirelson", title = "{Brownian} local minima, random dense countable sets and random equivalence classes", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "7:162--7:198", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-309", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/309", abstract = "A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically distributed. A framework for such concepts, proposed here, includes a wide class of random equivalence classes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; equivalence relation; local minimum; point process", } @Article{Picard:2006:BES, author = "Jean Picard", title = "{Brownian} excursions, stochastic integrals, and representation of {Wiener} functionals", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "8:199--8:248", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-310", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/310", abstract = "A stochastic calculus similar to Malliavin's calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the It{\^o} integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener functionals; this expression is an alternative to the classical Clark--Ocone formula. Moreover, this calculus enables to construct stochastic integrals of predictable or anticipating processes (forward, backward and symmetric integrals are considered).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "anticipating calculus; Brownian excursions; Malliavin calculus; stochastic integral representation; stochastic integrals", } @Article{Etore:2006:RWS, author = "Pierre Etor{\'e}", title = "On random walk simulation of one-dimensional diffusion processes with discontinuous coefficients", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "9:249--9:275", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-311", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/311", abstract = "In this paper, we provide a scheme for simulating one-dimensional processes generated by divergence or non-divergence form operators with discontinuous coefficients. We use a space bijection to transform such a process in another one that behaves locally like a Skew Brownian motion. Indeed the behavior of the Skew Brownian motion can easily be approached by an asymmetric random walk.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Monte Carlo methods, random walk, Skew Brownian motion, one-dimensional process, divergence form operator", } @Article{Bavouzet:2006:CGU, author = "Marie Pierre Bavouzet and Marouen Messaoud", title = "Computation of {Greeks} using {Malliavin}'s calculus in jump type market models", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "10:276--10:300", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-314", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/314", abstract = "We use the Malliavin calculus for Poisson processes in order to compute sensitivities for European and Asian options with underlying following a jump type diffusion. The main point is to settle an integration by parts formula (similar to the one in the Malliavin calculus) for a general multidimensional random variable which has an absolutely continuous law with differentiable density. We give an explicit expression of the differential operators involved in this formula and this permits to simulate them and consequently to run a Monte Carlo algorithm", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Asian options; compound Poisson process; Euler scheme; European options; Malliavin calculus; Monte-Carlo algorithm; sensitivity analysis", } @Article{Sellke:2006:RRR, author = "Thomas Sellke", title = "Recurrence of Reinforced Random Walk on a Ladder", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "11:301--11:310", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-313", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/313", abstract = "Consider reinforced random walk on a graph that looks like a doubly infinite ladder. All edges have initial weight 1, and the reinforcement convention is to add $ \delta > 0 $ to the weight of an edge upon first crossing, with no reinforcement thereafter. This paper proves recurrence for all $ \delta > 0 $. In so doing, we introduce a more general class of processes, termed multiple-level reinforced random walks.\par {\bf Editor's Note}. A draft of this paper was written in 1994. The paper is one of the first to make any progress on this type of reinforcement problem. It has motivated a substantial number of new and sometimes quite difficult studies of reinforcement models in pure and applied probability. The persistence of interest in models related to this has caused the original unpublished manuscript to be frequently cited, despite its lack of availability and the presence of errors. The opportunity to rectify this situation has led us to the somewhat unusual step of publishing a result that may have already entered the mathematical folklore.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "learning; Markov; martingale; multiple-level; Reinforced Random Walk", } @Article{Grigorescu:2006:TPL, author = "Ilie Grigorescu and Min Kang", title = "Tagged Particle Limit for a {Fleming--Viot} Type System", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "12:311--12:331", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-316", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/316", abstract = "We consider a branching system of $N$ Brownian particles evolving independently in a domain $D$ during any time interval between boundary hits. As soon as one particle reaches the boundary it is killed and one of the other particles splits into two independent particles, the complement of the set $D$ acting as a catalyst or hard obstacle. Identifying the newly born particle with the one killed upon contact with the catalyst, we determine the exact law of the tagged particle as $N$ approaches infinity. In addition, we show that any finite number of labelled particles become independent in the limit. Both results can be seen as scaling limits of a genome population undergoing redistribution present in the Fleming--Viot dynamics.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Fleming--Viot, propagation of chaos, tagged particle", } @Article{Deijfen:2006:NCR, author = "Maria Deijfen and Olle H{\"a}ggstr{\"o}m", title = "Nonmonotonic Coexistence Regions for the Two-Type {Richardson} Model on Graphs", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "13:331--13:344", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-321", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/321", abstract = "In the two-type Richardson model on a graph $ G = (V, E) $, each vertex is at a given time in state $0$, $1$ or $2$. A $0$ flips to a $1$ (resp.\ $2$) at rate $ \lambda_1$ ($ \lambda_2$) times the number of neighboring $1$'s ($2$'s), while $1$'s and $2$'s never flip. When $G$ is infinite, the main question is whether, starting from a single $1$ and a single $2$, with positive probability we will see both types of infection reach infinitely many sites. This has previously been studied on the $d$-dimensional cubic lattice $ Z^d$, $ d \geq 2$, where the conjecture (on which a good deal of progress has been made) is that such coexistence has positive probability if and only if $ \lambda_1 = \lambda_2$. In the present paper examples are given of other graphs where the set of points in the parameter space which admit such coexistence has a more surprising form. In particular, there exist graphs exhibiting coexistence at some value of $ \frac {\lambda_1}{\lambda_2} \neq 1$ and non-coexistence when this ratio is brought closer to $1$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coexistence; Competing growth; graphs", } @Article{Caravenna:2006:SAB, author = "Francesco Caravenna and Giambattista Giacomin and Lorenzo Zambotti", title = "Sharp asymptotic behavior for wetting models in (1+1)-dimension", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "14:345--14:362", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-320", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/320", abstract = "We consider continuous and discrete (1+1)-dimensional wetting models which undergo a localization/delocalization phase transition. Using a simple approach based on Renewal Theory we determine the precise asymptotic behavior of the partition function, from which we obtain the scaling limits of the models and an explicit construction of the infinite volume measure in all regimes, including the critical one.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Critical Wetting; delta-Pinning Model; Fluctuation Theory for Random Walks; Renewal Theory; Wetting Transition", } @Article{Limic:2006:SC, author = "Vlada Limic and Anja Sturm", title = "The spatial {$ \Lambda $}-coalescent", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "15:363--15:393", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-319", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/319", abstract = "This paper extends the notion of the $ \Lambda $-coalescent of Pitman (1999) to the spatial setting. The partition elements of the spatial $ \Lambda $-coalescent migrate in a (finite) geographical space and may only coalesce if located at the same site of the space. We characterize the $ \Lambda $-coalescents that come down from infinity, in an analogous way to Schweinsberg (2000). Surprisingly, all spatial coalescents that come down from infinity, also come down from infinity in a uniform way. This enables us to study space-time asymptotics of spatial $ \Lambda $-coalescents on large tori in $ d \geq 3$ dimensions. Some of our results generalize and strengthen the corresponding results in Greven et al. (2005) concerning the spatial Kingman coalescent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$la$-coalescent; coalescent; limit theorems, coalescing random walks; structured coalescent", } @Article{Basdevant:2006:FOP, author = "Anne-Laure Basdevant", title = "Fragmentation of Ordered Partitions and Intervals", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "16:394--16:417", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-323", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/323", abstract = "Fragmentation processes of exchangeable partitions have already been studied by several authors. This paper deals with fragmentations of exchangeable compositions, i.e., partitions of $ \mathbb {N} $ in which the order of the blocks matters. We will prove that such a fragmentation is bijectively associated to an interval fragmentation. Using this correspondence, we then study two examples: Ruelle's interval fragmentation and the interval fragmentation derived from the standard additive coalescent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "exchangeable compositions; Interval fragmentation", } @Article{Holroyd:2006:MTM, author = "Alexander Holroyd", title = "The Metastability Threshold for Modified Bootstrap Percolation in $d$ Dimensions", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "17:418--17:433", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-326", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/326", abstract = "In the modified bootstrap percolation model, sites in the cube $ \{ 1, \ldots, L \}^d $ are initially declared active independently with probability $p$. At subsequent steps, an inactive site becomes active if it has at least one active nearest neighbour in each of the $d$ dimensions, while an active site remains active forever. We study the probability that the entire cube is eventually active. For all $ d \geq 2$ we prove that as $ L \to \infty $ and $ p \to 0$ simultaneously, this probability converges to $1$ if $ L \geq \exp \cdots \exp \frac {\lambda + \epsilon }{p}$, and converges to $0$ if $ L \leq \exp \cdots \exp \frac {\lambda - \epsilon }{p}$, for any $ \epsilon > 0$. Here the exponential function is iterated $ d - 1$ times, and the threshold $ \lambda $ equals $ \pi^2 / 6$ for all $d$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bootstrap percolation; cellular automaton; finite-size scaling; metastability", } @Article{Nane:2006:LIL, author = "Erkan Nane", title = "Laws of the iterated logarithm for $ \alpha $-time {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "18:434--18:459", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-327", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/327", abstract = "We introduce a class of iterated processes called $ \alpha $-time Brownian motion for $ 0 < \alpha \leq 2$. These are obtained by taking Brownian motion and replacing the time parameter with a symmetric $ \alpha $-stable process. We prove a Chung-type law of the iterated logarithm (LIL) for these processes which is a generalization of LIL proved in {citehu} for iterated Brownian motion. When $ \alpha = 1$ it takes the following form\par $$ \liminf_{T \to \infty } \ T^{-1 / 2}(\log \log T) \sup_{0 \leq t \leq T}|Z_t| = \pi^2 \sqrt {\lambda_1} \quad a.s. $$ where $ \lambda_1$ is the first eigenvalue for the Cauchy process in the interval $ [ - 1, 1].$ We also define the local time $ L^*(x, t)$ and range $ R^*(t) = |{x \colon Z(s) = x \text { for some } s \leq t}|$ for these processes for $ 1 < \alpha < 2$. We prove that there are universal constants $ c_R, c_L \in (0, \infty) $ such that\par $$ \limsup_{t \to \infty } \frac {R^*(t)}{(t / \log \log t)^{1 / 2 \alpha } \log \log t} = c_R \quad a.s. $$ $$ \liminf_{t \to \infty } \frac {\sup_{x \in {R}}L^*(x, t)}{(t / \log \log t)^{1 - 1 / 2 \alpha }} = c_L \quad a.s. $$", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, symmetric $alpha$-stable process, $alpha$-time Brownian motion, local time, Chung's law, Kesten's law", } @Article{Adams:2006:LSP, author = "Stefan Adams and Jean-Bernard Bru and Wolfgang Koenig", title = "Large systems of path-repellent {Brownian} motions in a trap at positive temperature", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "19:460--19:485", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-330", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/330", abstract = "We study a model of $N$ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from escaping to infinity, and a pair-interaction Hamiltonian, which imposes a repellency of the $N$ paths. In fact, this interaction is an $N$-dependent regularisation of the Brownian intersection local times, an object which is of independent interest in the theory of stochastic processes. The time horizon (interpreted as the inverse temperature) is kept fixed. We analyse the model for diverging number of Brownian motions in terms of a large deviation principle. The resulting variational formula is the positive-temperature analogue of the well-known Gross--Pitaevskii formula, which approximates the ground state of a certain dilute large quantum system; the kinetic energy term of that formula is replaced by a probabilistic energy functional. This study is a continuation of the analysis in [ABK06] where we considered the limit of diverging time (i.e., the zero-temperature limit) with fixed number of Brownian motions, followed by the limit for diverging number of motions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian intersection local times; Gross--Pitaevskii formula; Interacting Brownian motions; large deviations; occupation measure", } @Article{Klein:2006:CCI, author = "Thierry Klein and Yutao Ma and Nicolas Privault", title = "Convex Concentration Inequalities and Forward--Backward Stochastic Calculus", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "20:486--20:512", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-332", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/332", abstract = "Given $ (M_t)_{t \in \mathbb {R}_+} $ and $ (M^*_t)_{t \in \mathbb {R}_+} $ respectively a forward and a backward martingale with jumps and continuous parts, we prove that $ E[\phi (M_t + M^*_t)] $ is non-increasing in $t$ when $ \phi $ is a convex function, provided the local characteristics of $ (M_t)_{t \in \mathbb {R}_+}$ and $ (M^*_t)_{t \in \mathbb {R}_+}$ satisfy some comparison inequalities. We deduce convex concentration inequalities and deviation bounds for random variables admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Convex concentration inequalities, forward--backward stochastic calculus, deviation inequalities, Clark formula, Brownian motion, jump processes", } @Article{Maximilian:2006:EMD, author = "Duerre Maximilian", title = "Existence of multi-dimensional infinite volume self-organized critical forest-fire models", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "21:513--21:539", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-333", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/333", abstract = "Consider the following forest-fire model where the possible locations of trees are the sites of a cubic lattice. Each site has two possible states: 'vacant' or 'occupied'. Vacant sites become occupied according to independent rate 1 Poisson processes. Independently, at each site ignition (by lightning) occurs according to independent rate lambda Poisson processes. When a site is ignited, its occupied cluster becomes vacant instantaneously. If the lattice is one-dimensional or finite, then with probability one, at each time the state of a given site only depends on finitely many Poisson events; a process with the above description can be constructed in a standard way. If the lattice is infinite and multi-dimensional, in principle, the state of a given site can be influenced by infinitely many Poisson events in finite time.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "existence; forest-fire model; forest-fires; self-organized criticality; well-defined", } @Article{Schmitz:2006:ECD, author = "Tom Schmitz", title = "Examples of Condition {$ (T) $} for Diffusions in a Random Environment", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "22:540--22:562", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-337", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/337", abstract = "With the help of the methods developed in our previous article [Schmitz, to appear in Annales de l'I.H.P., in press], we highlight condition $ (T) $ as a source of new examples of 'ballistic' diffusions in a random environment when $ d > 1 $ ('ballistic' means that a strong law of large numbers with non-vanishing limiting velocity holds). In particular we are able to treat the case of non-constant diffusion coefficients, a feature that causes problems. Further we recover the ballistic character of two important classes of diffusions in a random environment by simply checking condition $ (T) $. This not only points out to the broad range of examples where condition $ (T) $ can be checked, but also fortifies our belief that condition $ (T) $ is a natural contender for the characterisation of ballistic diffusions in a random environment when $ d > 1 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Diffusions in a random environment, ballistic behavior, Condition $(T)$", } @Article{Kim:2006:PSD, author = "Kyeong-Hun Kim", title = "Parabolic {SPDEs} Degenerating on the Boundary of Non-Smooth Domain", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "23:563--23:584", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-339", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/339", abstract = "Degenerate stochastic partial differential equations of divergence and non-divergence forms are considered in non-smooth domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Holder estimates of the solutions are presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "SPDEs degenerating on the boundary; weighted Sobolev spaces", } @Article{Swart:2006:RAC, author = "Jan Swart and Klaus Fleischmann", title = "Renormalization analysis of catalytic {Wright--Fisher} diffusions", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "24:585--24:654", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-341", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/341", abstract = "Recently, several authors have studied maps where a function, describing the local diffusion matrix of a diffusion process with a linear drift towards an attraction point, is mapped into the average of that function with respect to the unique invariant measure of the diffusion process, as a function of the attraction point. Such mappings arise in the analysis of infinite systems of diffusions indexed by the hierarchical group, with a linear attractive interaction between the components. In this context, the mappings are called renormalization transformations. We consider such maps for catalytic Wright--Fisher diffusions. These are diffusions on the unit square where the first component (the catalyst) performs an autonomous Wright--Fisher diffusion, while the second component (the reactant) performs a Wright--Fisher diffusion with a rate depending on the first component through a catalyzing function. We determine the limit of rescaled iterates of renormalization transformations acting on the diffusion matrices of such catalytic Wright--Fisher diffusions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Renormalization, catalytic Wright--Fisher diffusion, embedded particle system, extinction, unbounded growth, interacting diffusions, universality", } @Article{Berger:2006:TPC, author = "Noam Berger and Itai Benjamini and Omer Angel and Yuval Peres", title = "Transience of percolation clusters on wedges", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "25:655--25:669", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-345", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/345", abstract = "We study random walks on supercritical percolation clusters on wedges in $ Z^3 $, and show that the infinite percolation cluster is (a.s.) transient whenever the wedge is transient. This solves a question raised by O. H{\"a}ggstr{\"o}m and E. Mossel. We also show that for convex gauge functions satisfying a mild regularity condition, the existence of a finite energy flow on $ Z^2 $ is equivalent to the (a.s.) existence of a finite energy flow on the supercritical percolation cluster. This answers a question of C. Hoffman.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "percolation; transience; wedges", } @Article{Cator:2006:BSC, author = "Eric Cator and Sergei Dobrynin", title = "Behavior of a second class particle in {Hammersley}'s process", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "26:670--26:685", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-340", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/340", abstract = "In the case of a rarefaction fan in a non-stationary Hammersley process, we explicitly calculate the asymptotic behavior of the process as we move out along a ray, and the asymptotic distribution of the angle within the rarefaction fan of a second class particle and a dual second class particle. Furthermore, we consider a stationary Hammersley process and use the previous results to show that trajectories of a second class particle and a dual second class particles touch with probability one, and we give some information on the area enclosed by the two trajectories, up until the first intersection point. This is linked to the area of influence of an added Poisson point in the plane.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Hammersley's process; rarefaction fan; second class particles", } @Article{Odasso:2006:SSS, author = "Cyril Odasso", title = "Spatial Smoothness of the Stationary Solutions of the {$3$D} {Navier--Stokes} Equations", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "27:686--27:699", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-336", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/336", abstract = "We consider stationary solutions of the three dimensional Navier--Stokes equations (NS3D) with periodic boundary conditions and driven by an external force which might have a deterministic and a random part. The random part of the force is white in time and very smooth in space. We investigate smoothness properties in space of the stationary solutions. Classical technics for studying smoothness of stochastic PDEs do not seem to apply since global existence of strong solutions is not known. We use the Kolmogorov operator and Galerkin approximations. We first assume that the noise has spatial regularity of order $p$ in the $ L^2$ based Sobolev spaces, in other words that its paths are in $ H^p$. Then we prove that at each fixed time the law of the stationary solutions is supported by $ H^{p + 1}$. Then, using a totally different technic, we prove that if the noise has Gevrey regularity then at each fixed time, the law of a stationary solution is supported by a Gevrey space. Some information on the Kolmogorov dissipation scale is deduced.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic three-dimensional Navier--Stokes equations, invariant measure", } @Article{Dereich:2006:HRQ, author = "Steffen Dereich and Michael Scheutzow", title = "High Resolution Quantization and Entropy Coding for Fractional {Brownian} Motion", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "28:700--28:722", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-344", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/344", abstract = "We establish the precise asymptotics of the quantization and entropy coding errors for fractional Brownian motion with respect to the supremum norm and $ L^p [0, 1]$-norm distortions. We show that all moments in the quantization problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremum-norm distortion, our proof uses an explicit construction of efficient codebooks based on a particular entropy constrained coding scheme.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "complexity; distortion rate function; entropy; High-resolution quantization; stochastic process", } @Article{Fleischmann:2006:HLF, author = "Klaus Fleischmann and Peter M{\"o}rters and Vitali Wachtel", title = "Hydrodynamic Limit Fluctuations of Super-{Brownian} Motion with a Stable Catalyst", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "29:723--29:767", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-348", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/348", abstract = "We consider the behaviour of a continuous super-Brownian motion catalysed by a random medium with infinite overall density under the hydrodynamic scaling of mass, time, and space. We show that, in supercritical dimensions, the scaled process converges to a macroscopic heat flow, and the appropriately rescaled random fluctuations around this macroscopic flow are asymptotically bounded, in the sense of log-Laplace transforms, by generalised stable Ornstein--Uhlenbeck processes. The most interesting new effect we observe is the occurrence of an index-jump from a Gaussian situation to stable fluctuations of index $ 1 + \gamma $, where $ \gamma \in (0, 1) $ is an index associated to the medium.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Catalyst, reactant, superprocess, critical scaling, refined law of large numbers, catalytic branching, stable medium, random environment, supercritical dimension, generalised stable Ornstein--Uhlenbeck process, index jump, parabolic Anderson model with sta", } @Article{Belhaouari:2006:CRS, author = "Samir Belhaouari and Thomas Mountford and Rongfeng Sun and Glauco Valle", title = "Convergence Results and Sharp Estimates for the Voter Model Interfaces", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "30:768--30:801", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-349", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/349", abstract = "We study the evolution of the interface for the one-dimensional voter model. We show that if the random walk kernel associated with the voter model has finite $ \gamma $-th moment for some $ \gamma > 3$, then the evolution of the interface boundaries converge weakly to a Brownian motion under diffusive scaling. This extends recent work of Newman, Ravishankar and Sun. Our result is optimal in the sense that finite $ \gamma $-th moment is necessary for this convergence for all $ \gamma \in (0, 3)$. We also obtain relatively sharp estimates for the tail distribution of the size of the equilibrium interface, extending earlier results of Cox and Durrett, and Belhaouari, Mountford and Valle.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "voter model interface, coalescing random walks, Brownian web, invariance principle", } @Article{Sabot:2006:RWD, author = "Christophe Sabot and Nathana{\"e}l Enriquez", title = "Random Walks in a {Dirichlet} Environment", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "31:802--31:816", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-350", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/350", abstract = "This paper states a law of large numbers for a random walk in a random iid environment on $ Z^d $, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the asymptotic velocity of the process and also an asymptotic expansion of this velocity at low disorder.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random Walks, Random Environments, Dirichlet Laws, Reinforced Random Walks", } @Article{Xiao:2006:SLN, author = "Yimin Xiao and Davar Khoshnevisan and Dongsheng Wu", title = "Sectorial Local Non-Determinism and the Geometry of the {Brownian} Sheet", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "32:817--32:843", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-353", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/353", abstract = "We prove the following results about the images and multiple points of an $N$-parameter, $d$-dimensional Brownian sheet $ B = \{ B(t) \}_{t \in R_+^N}$: (1) If $ \text {dim}_H F \leq d / 2$, then $ B(F)$ is almost surely a Salem set.\par (2) If $ N \leq d / 2$, then with probability one $ \text {dim}_H B(F) = 2 \text {dim} F$ for all Borel sets of $ R_+^N$, where ``$ \text {dim}_H$'' could be everywhere replaced by the ``Hausdorff, '' ``packing, '' ``upper Minkowski, '' or ``lower Minkowski dimension.''\par (3) Let $ M_k$ be the set of $k$-multiple points of $B$. If $ N \leq d / 2$ and $ N k > (k - 1)d / 2$, then $ \text {dim}_H M_k = \text {dim}_p M_k = 2 N k - (k - 1)d$, a.s.\par The Hausdorff dimension aspect of (2) was proved earlier; see Mountford (1989) and Lin (1999). The latter references use two different methods; ours of (2) are more elementary, and reminiscent of the earlier arguments of Monrad and Pitt (1987) that were designed for studying fractional Brownian motion. If $ N > d / 2$ then (2) fails to hold. In that case, we establish uniform-dimensional properties for the $ (N, 1)$-Brownian sheet that extend the results of Kaufman (1989) for 1-dimensional Brownian motion. Our innovation is in our use of the {\em sectorial local nondeterminism} of the Brownian sheet (Khoshnevisan and Xiao, 2004).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian sheet, sectorial local nondeterminism, image, Salem sets, multiple points, Hausdorff dimension, packing dimension", } @Article{Dony:2006:WUC, author = "Julia Dony and Uwe Einmahl", title = "Weighted uniform consistency of kernel density estimators with general bandwidth sequences", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "33:844--33:859", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-354", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/354", abstract = "Let $ f_{n, h} $ be a kernel density estimator of a continuous and bounded $d$-dimensional density $f$. Let $ \psi (t)$ be a positive continuous function such that $ \| \psi f^\beta \|_\infty < \infty $ for some $ 0 < \beta < 1 / 2$. We are interested in the rate of consistency of such estimators with respect to the weighted sup-norm determined by $ \psi $. This problem has been considered by Gin, Koltchinskii and Zinn (2004) for a deterministic bandwidth $ h_n$. We provide ``uniform in $h$'' versions of some of their results, allowing us to determine the corresponding rates of consistency for kernel density estimators where the bandwidth sequences may depend on the data and/or the location.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "convergence rates; empirical process; kernel density estimator; uniform in bandwidth; weighted uniform consistency", } @Article{Feyel:2006:CIA, author = "Denis Feyel and Arnaud {de La Pradelle}", title = "Curvilinear Integrals Along Enriched Paths", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "34:860--34:892", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-356", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/356", abstract = "Inspired by the fundamental work of T. J. Lyons, we develop a theory of curvilinear integrals along a new kind of enriched paths in $ R^d $. We apply these methods to the fractional Brownian Motion, and prove a support theorem for SDE driven by the Skorohod fBM of Hurst parameter $ H > 1 / 4 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Curvilinear integrals, H{\"o}lder continuity, rough paths, stochastic integrals, stochastic differential equations, fractional Brownian motion.", } @Article{Wagner:2006:PGB, author = "Wolfgang Wagner", title = "Post-gelation behavior of a spatial coagulation model", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "35:893--35:933", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-359", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/359", abstract = "A coagulation model on a finite spatial grid is considered. Particles of discrete masses jump randomly between sites and, while located at the same site, stick together according to some coagulation kernel. The asymptotic behavior (for increasing particle numbers) of this model is studied in the situation when the coagulation kernel grows sufficiently fast so that the phenomenon of gelation is observed. Weak accumulation points of an appropriate sequence of measure-valued processes are characterized in terms of solutions of a nonlinear equation. A natural description of the behavior of the gel is obtained by using the one-point compactification of the size space. Two aspects of the limiting equation are of special interest. First, for a certain class of coagulation kernels, this equation differs from a naive extension of Smoluchowski's coagulation equation. Second, due to spatial inhomogeneity, an equation for the time evolution of the gel mass density has to be added. The jump rates are assumed to vanish with increasing particle masses so that the gel is immobile. Two different gel growth mechanisms (active and passive gel) are found depending on the type of the coagulation kernel.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "post-gelation behavior; Spatial coagulation model; stochastic particle systems", } @Article{Ramanan:2006:RDD, author = "Kavita Ramanan", title = "Reflected Diffusions Defined via the Extended {Skorokhod} Map", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "36:934--36:992", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-360", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/360", abstract = "This work introduces the extended Skorokhod problem (ESP) and associated extended Skorokhod map (ESM) that enable a pathwise construction of reflected diffusions that are not necessarily semimartingales. Roughly speaking, given the closure $G$ of an open connected set in $ {\mathbb R}^J$, a non-empty convex cone $ d(x) \subset {\mathbb R}^J$ specified at each point $x$ on the boundary $ \partial G$, and a c{\`a}dl{\`a}g trajectory $ \psi $ taking values in $ {\mathbb R}^J$, the ESM $ \bar \Gamma $ defines a constrained version $ \phi $ of $ \psi $ that takes values in $G$ and is such that the increments of $ \phi - \psi $ on any interval $ [s, t]$ lie in the closed convex hull of the directions $ d(\phi (u)), u \in (s, t]$. When the graph of $ d(\cdot)$ is closed, the following three properties are established: (i) given $ \psi $, if $ (\phi, \eta)$ solve the ESP then $ (\phi, \eta)$ solve the corresponding Skorokhod problem (SP) if and only if $ \eta $ is of bounded variation; (ii) given $ \psi $, any solution $ (\phi, \eta)$ to the ESP is a solution to the SP on the interval $ [0, \tau_0)$, but not in general on $ [0, \tau_0]$, where $ \tau_0$ is the first time that $ \phi $ hits the set $ {\cal V}$ of points $ x \in \partial G$ such that $ d(x)$ contains a line; (iii) the graph of the ESM $ \bar \Gamma $ is closed on the space of c{\`a}dl{\`a}g trajectories (with respect to both the uniform and the $ J_1$-Skorokhod topologies).\par The paper then focuses on a class of multi-dimensional ESPs on polyhedral domains with a non-empty $ {\cal V}$-set. Uniqueness and existence of solutions for this class of ESPs is established and existence and pathwise uniqueness of strong solutions to the associated stochastic differential equations with reflection is derived. The associated reflected diffusions are also shown to satisfy the corresponding submartingale problem. Lastly, it is proved that these reflected diffusions are semimartingales on $ [0, \tau_0]$. One motivation for the study of this class of reflected diffusions is that they arise as approximations of queueing networks in heavy traffic that use the so-called generalised processor sharing discipline.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "reflected diffusions; Skorokhod problem; stochastic differential equations; submartingale problem", } @Article{Bass:2006:MDL, author = "Richard Bass and Xia Chen and Jay Rosen", title = "Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "37:993--37:1030", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-362", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/362", abstract = "We study moderate deviations for the renormalized self-intersection local time of planar random walks. We also prove laws of the iterated logarithm for such local times.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; Gagliardo--Nirenberg; intersection local time; large deviations; law of the iterated logarithm; moderate deviations; planar random walks", } @Article{Gapeev:2006:DOS, author = "Pavel Gapeev", title = "Discounted optimal stopping for maxima in diffusion models with finite horizon", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "38:1031--38:1048", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-367", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/367", abstract = "We present a solution to some discounted optimal stopping problem for the maximum of a geometric Brownian motion on a finite time interval. The method of proof is based on reducing the initial optimal stopping problem with the continuation region determined by an increasing continuous boundary surface to a parabolic free-boundary problem. Using the change-of-variable formula with local time on surfaces we show that the optimal boundary can be characterized as a unique solution of a nonlinear integral equation. The result can be interpreted as pricing American fixed-strike lookback option in a diffusion model with finite time horizon.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "a change-of-varia; a nonlinear Volterra integral equation of the second kind; boundary surface; Discounted optimal stopping problem; finite horizon; geometric Brownian motion; maximum process; normal reflection; parabolic free-boundary problem; smooth fit", } @Article{Pinelis:2006:NDS, author = "Iosif Pinelis", title = "On normal domination of (super)martingales", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "39:1049--39:1070", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-371", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/371", abstract = "Let $ (S_0, S_1, \dots) $ be a supermartingale relative to a nondecreasing sequence of $ \sigma $-algebras $ (H_{\le 0}, H_{\le 1}, \dots)$, with $ S_0 \leq 0$ almost surely (a.s.) and differences $ X_i := S_i - S_{i - 1}$. Suppose that for every $ i = 1, 2, \dots $ there exist $ H_{\le (i - 1)}$-measurable r.v.'s $ C_{i - 1}$ and $ D_{i - 1}$ and a positive real number $ s_i$ such that $ C_{i - 1} \leq X_i \le D_{i - 1}$ and $ D_{i - 1} - C_{i - 1} \leq 2 s_i$ a.s. Then for all real $t$ and natural $n$ and all functions $f$ satisfying certain convexity conditions $ E f(S_n) \leq E f(s Z)$, where $ f_t(x) := \max (0, x - t)^5$, $ s := \sqrt {s_1^2 + \dots + s_n^2}$, and $ Z \sim N(0, 1)$. In particular, this implies $ P(S_n \ge x) \le c_{5, 0}P(s Z \ge x) \quad \forall x \in R$, where $ c_{5, 0} = 5 !(e / 5)^5 = 5.699 \dots $. Results for $ \max_{0 \leq k \leq n}S_k$ in place of $ S_n$ and for concentration of measure also follow.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "generalized moments; martingales; probability inequalities; supermartingales; upper bounds", } @Article{Chazottes:2006:REW, author = "Jean-Ren{\'e} Chazottes and Cristian Giardina and Frank Redig", title = "Relative entropy and waiting times for continuous-time {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "40:1049--40:1068", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-374", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/374", abstract = "For discrete-time stochastic processes, there is a close connection between return (resp. waiting) times and entropy (resp. relative entropy). Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one needs a reference measure on path space and so the natural object is relative entropy rather than entropy. In this paper we elaborate on this in the case of continuous-time Markov processes with finite state space. A reference measure of special interest is the one associated to the time-reversed process. In that case relative entropy is interpreted as the entropy production rate. The main results of this paper are: almost-sure convergence to relative entropy of the logarithm of waiting-times ratios suitably normalized, and their fluctuation properties (central limit theorem and large deviation principle).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "continuous-time Markov chain, law of large numbers, central limit theorem, large deviations, entropy production, time-reversed process", } @Article{Zhan:2006:SPA, author = "Dapeng Zhan", title = "Some Properties of Annulus {SLE}", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "41:1069--41:1093", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-338", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/338", abstract = "An annulus SLE$_\kappa $ trace tends to a single point on the target circle, and the density function of the end point satisfies some differential equation. Some martingales or local martingales are found for annulus SLE$_4$, SLE$_8$ and SLE$_8 / 3$. From the local martingale for annulus SLE$_4$ we find a candidate of discrete lattice model that may have annulus SLE$_4$ as its scaling limit. The local martingale for annulus SLE$_8 / 3$ is similar to those for chordal and radial SLE$_8 / 3$. But it seems that annulus SLE$_8 / 3$ does not satisfy the restriction property", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "continuum scaling limit, percolation, SLE, conformal invariance", } @Article{Balazs:2006:CRF, author = "Marton Balazs and Eric Cator and Timo Seppalainen", title = "Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "42:1094--42:1132", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-366", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/366", abstract = "We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right after its jump we prove that the variance of the last-passage time in a characteristic direction is of order $ t^{2 / 3} $. With more general boundary conditions that include the rarefaction fan case we show that the last-passage time fluctuations are still of order $ t^{1 / 3} $, and also that the transversal fluctuations of the maximal path have order $ t^{2 / 3} $. We adapt and then build on a recent study of Hammersley's process by Cator and Groeneboom, and also utilize the competition interface introduced by Ferrari, Martin and Pimentel. The arguments are entirely probabilistic, and no use is made of the combinatorics of Young tableaux or methods of asymptotic analysis.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Burke's theorem; competition interface; cube root asymptotics; Last-passage; rarefaction fan; simple exclusion", } @Article{Brouwer:2006:CSD, author = "Rachel Brouwer and Juho Pennanen", title = "The Cluster Size Distribution for a Forest-Fire Process on {$Z$}", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "43:1133--43:1143", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-369", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/369", abstract = "Consider the following forest-fire model where trees are located on sites of $ \mathbb {Z} $. A site can be vacant or be occupied by a tree. Each vacant site becomes occupied at rate $1$, independently of the other sites. Each site is hit by lightning with rate $ \lambda $, which burns down the occupied cluster of that site instantaneously. As $ \lambda \downarrow 0$ this process is believed to display self-organised critical behaviour.\par This paper is mainly concerned with the cluster size distribution in steady-state. Drossel, Clar and Schwabl (1993) claimed that the cluster size distribution has a certain power law behaviour which holds for cluster sizes that are not too large compared to some explicit cluster size $ s_{max}$. The latter can be written in terms of $ \lambda $ approximately as $ s_{max} \ln (s_{max}) = 1 / \lambda $. However, Van den Berg and Jarai (2005) showed that this claim is not correct for cluster sizes of order $ s_{max}$, which left the question for which cluster sizes the power law behaviour {\em does} hold. Our main result is a rigorous proof of the power law behaviour up to cluster sizes of the order $ s_{max}^{1 / 3}$. Further, it proves the existence of a stationary translation invariant distribution, which was always assumed but never shown rigorously in the literature.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "forest-fires, self-organised criticality, cluster size distribution", } @Article{Shiga:2006:IDR, author = "Tokuzo Shiga and Hiroshi Tanaka", title = "Infinitely Divisible Random Probability Distributions with an Application to a Random Motion in a Random Environment", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "44:1144--44:1183", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-380", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/380", abstract = "The infinite divisibility of probability distributions on the space $ P (R) $ of probability distributions on $R$ is defined and related fundamental results such as the L{\'e}vy--Khintchin formula, representation of It{\^o} type of infinitely divisible RPD, stable RPD and Levy processes on $ P (R)$ are obtained. As an application we investigate limiting behaviors of a simple model of a particle motion in a random environment", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "infinite divisibility; L{\'e}vy-It{\^o} repr{\'e}sentation; L{\'e}vy-Khintchin representation; random environment; random probability distribution", } @Article{Bertacchi:2006:ABS, author = "Daniela Bertacchi", title = "Asymptotic Behaviour of the Simple Random Walk on the $2$-dimensional Comb", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "45:1184--45:1203", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-377", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/377", abstract = "We analyze the differences between the horizontal and the vertical component of the simple random walk on the 2-dimensional comb. In particular we evaluate by combinatorial methods the asymptotic behaviour of the expected value of the distance from the origin, the maximal deviation and the maximal span in $n$ steps, proving that for all these quantities the order is $ n^{1 / 4}$ for the horizontal projection and $ n^{1 / 2}$ for the vertical one (the exact constants are determined). Then we rescale the two projections of the random walk dividing by $ n^{1 / 4}$ and $ n^{1 / 2}$ the horizontal and vertical ones, respectively. The limit process is obtained. With similar techniques the walk dimension is determined, showing that the Einstein relation between the fractal, spectral and walk dimensions does not hold on the comb.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian Motion; Comb; Generating Function; Maximal Excursion; Random Walk", } @Article{Lifshits:2006:SDG, author = "Mikhail Lifshits and Werner Linde and Zhan Shi", title = "Small Deviations of {Gaussian} Random Fields in {$ L_q $}-Spaces", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "46:1204--46:1233", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-379", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/379", abstract = "We investigate small deviation properties of Gaussian random fields in the space $ L_q(R^N, \mu) $ where $ \mu $ is an arbitrary finite compactly supported Borel measure. Of special interest are hereby ``thin'' measures $ \mu $, i.e., those which are singular with respect to the $N$--dimensional Lebesgue measure; the so-called self-similar measures providing a class of typical examples. For a large class of random fields (including, among others, fractional Brownian motions), we describe the behavior of small deviation probabilities via numerical characteristics of $ \mu $, called mixed entropy, characterizing size and regularity of $ \mu $. For the particularly interesting case of self-similar measures $ \mu $, the asymptotic behavior of the mixed entropy is evaluated explicitly. As a consequence, we get the asymptotic of the small deviation for $N$-parameter fractional Brownian motions with respect to $ L_q(R^N, \mu)$-norms. While the upper estimates for the small deviation probabilities are proved by purely probabilistic methods, the lower bounds are established by analytic tools concerning Kolmogorov and entropy numbers of Holder operators.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractal measures; fractional Brownian motion; Gaussian random fields; Kolmogorov numbers; metric entropy", } @Article{Barbour:2006:DSW, author = "Andrew Barbour and Gesine Reinert", title = "Discrete small world networks", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "47:1234--47:1283", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-381", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/381", abstract = "Small world models are networks consisting of many local links and fewer long range `shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution of typical inter-point network distances. We establish approximations to the distribution of the graph distance in a discrete ring network with extra random links, and compare the results to those for simpler models, in which the extra links have zero length and the ring is continuous.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Small-world networks, shortest path length, branching process", } @Article{Su:2006:GFC, author = "Zhonggen Su", title = "{Gaussian} Fluctuations in Complex Sample Covariance Matrices", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "48:1284--48:1320", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-378", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/378", abstract = "Let $ X = (X_{i, j})_{m \times n}, m \ge n $, be a complex Gaussian random matrix with mean zero and variance $ \frac 1 n $, let $ S = X^*X $ be a sample covariance matrix. In this paper we are mainly interested in the limiting behavior of eigenvalues when $ \frac m n \rightarrow \gamma \ge 1 $ as $ n \rightarrow \infty $. Under certain conditions on $k$, we prove the central limit theorem holds true for the $k$-th largest eigenvalues $ \lambda_{(k)}$ as $k$ tends to infinity as $ n \rightarrow \infty $. The proof is largely based on the Costin--Lebowitz--Soshnikov argument and the asymptotic estimates for the expectation and variance of the number of eigenvalues in an interval. The standard technique for the RH problem is used to compute the exact formula and asymptotic properties for the mean density of eigenvalues. As a by-product, we obtain a convergence speed of the mean density of eigenvalues to the Marchenko--Pastur distribution density under the condition $ | \frac m n - \gamma | = O(\frac 1 n)$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central limit theorem; Eigenvalues; RH problems; Sample covariance matrices; the Costin--Lebowitz--Soshnikov theorem", } @Article{Chaumont:2006:LEP, author = "Loic Chaumont and Juan Carlos Pardo Millan", title = "The Lower Envelope of Positive Self-Similar {Markov} Processes", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "49:1321--49:1341", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-382", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/382", abstract = "We establish integral tests and laws of the iterated logarithm for the lower envelope of positive self-similar Markov processes at 0 and $ + \infty $. Our proofs are based on the Lamperti representation and time reversal arguments. These results extend laws of the iterated logarithm for Bessel processes due to Dvoretzky and Erdos (1951), Motoo (1958), and Rivero (2003).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Self-similar Markov process, L'evy process, Lamperti representation, last passage time, time reversal, integral test, law of the iterated logarithm", } @Article{Johansson:2006:EGM, author = "Kurt Johansson and Eric Nordenstam", title = "Eigenvalues of {GUE} Minors", journal = j-ELECTRON-J-PROBAB, volume = "11", pages = "50:1342--50:1371", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v11-370", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See erratum \cite{Johansson:2007:EEG}.", URL = "http://ejp.ejpecp.org/article/view/370", abstract = "Consider an infinite random matrix $ H = (h_{ij})_{0 < i, j} $ picked from the Gaussian Unitary Ensemble (GUE). Denote its main minors by $ H_i = (h_{rs})_{1 \leq r, s \leq i} $ and let the $j$:th largest eigenvalue of $ H_i$ be $ \mu^i_j$. We show that the configuration of all these eigenvalues $ (i, \mu_j^i)$ form a determinantal point process on $ \mathbb {N} \times \mathbb {R}$.\par Furthermore we show that this process can be obtained as the scaling limit in random tilings of the Aztec diamond close to the boundary. We also discuss the corresponding limit for random lozenge tilings of a hexagon.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random matrices; Tiling problems", } @Article{Bass:2007:FPR, author = "Richard Bass and Jay Rosen", title = "Frequent Points for Random Walks in Two Dimensions", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "1:1--1:46", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-388", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/388", abstract = "For a symmetric random walk in $ Z^2 $ which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the Erd{\H{o}}s--Taylor conjecture and obtain the asymptotics for the number of visits to the most visited site. We also obtain the asymptotics for the number of points which are visited very frequently by time $n$. Among the tools we use are Harnack inequalities and Green's function estimates for random walks with unbounded jumps; some of these are of independent interest.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walks, Green's functions, Harnack inequalities, frequent points", } @Article{Ivanoff:2007:CCP, author = "B. Gail Ivanoff and Ely Merzbach and Mathieu Plante", title = "A Compensator Characterization of Point Processes on Topological Lattices", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "2:47--2:74", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-390", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/390", abstract = "We resolve the longstanding question of how to define the compensator of a point process on a general partially ordered set in such a way that the compensator exists, is unique, and characterizes the law of the process. We define a family of one-parameter compensators and prove that this family is unique in some sense and characterizes the finite dimensional distributions of a totally ordered point process. This result can then be applied to a general point process since we prove that such a process can be embedded into a totally ordered point process on a larger space. We present some examples, including the partial sum multiparameter process, single line point processes, multiparameter renewal processes, and obtain a new characterization of the two-parameter Poisson process", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "point process, compensator, partial order, single jump process, partial sum process, adapted random set, renewal process, Poisson process, multiparameter martingale", } @Article{Luczak:2007:ADC, author = "Malwina Luczak and Colin McDiarmid", title = "Asymptotic distributions and chaos for the supermarket model", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "3:75--3:99", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-391", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/391", abstract = "In the supermarket model there are $n$ queues, each with a unit rate server. Customers arrive in a Poisson process at rate $ \lambda n$, where $ 0 < \lambda < 1$. Each customer chooses $ d \geq 2$ queues uniformly at random, and joins a shortest one. It is known that the equilibrium distribution of a typical queue length converges to a certain explicit limiting distribution as $ n \to \infty $. We quantify the rate of convergence by showing that the total variation distance between the equilibrium distribution and the limiting distribution is essentially of order $ 1 / n$ and we give a corresponding result for systems starting from quite general initial conditions (not in equilibrium). Further, we quantify the result that the systems exhibit chaotic behaviour: we show that the total variation distance between the joint law of a fixed set of queue lengths and the corresponding product law is essentially of order at most $ 1 / n$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Supermarket model, join the shortest queue, random choices, power of two choices, load balancing, equilibrium, concentration of measure, law of large numbers, chaos", } @Article{Mendez:2007:ETS, author = "Pedro Mendez", title = "Exit Times of Symmetric Stable Processes from Unbounded Convex Domains", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "4:100--4:121", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-393", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/393", abstract = "We provide several inequalities on the asymptotic behavior of the harmonic measure of the first exit position of a $d$-dimensional symmetric stable process from a unbounded convex domain. Our results on the harmonic measure will determine the asymptotic behavior of the distributions of the first exit time from the domain. These inequalities are given in terms of the growth of the in radius of the cross sections of the domain.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stable process, exit times, unbounded domains", } @Article{Heveling:2007:PSC, author = "Matthias Heveling and Gunter Last", title = "Point shift characterization of {Palm} measures on {Abelian} groups", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "5:122--5:137", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-394", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/394", abstract = "Our first aim in this paper is to characterize Palm measures of stationary point processes through point stationarity. This generalizes earlier results from the Euclidean case to the case of an Abelian group. While a stationary point process looks statistically the same from each site, a point stationary point process looks statistically the same from each of its points. Even in the Euclidean case our proof will simplify some of the earlier arguments. A new technical result of some independent interest is the existence of a complete countable family of matchings. Using a change of measure we will generalize our results to discrete random measures. In the Euclidean case we will finally treat general random measures by means of a suitable approximation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "point process, random measure, stationarity, point-stationarity, Palm measure, matching, bijective point map", } @Article{Uchiyama:2007:AEG, author = "Kouhei Uchiyama", title = "Asymptotic Estimates of the {Green} Functions and Transition Probabilities for {Markov} Additive Processes", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "6:138--6:180", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-396", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/396", abstract = "In this paper we shall derive asymptotic expansions of the Green function and the transition probabilities of Markov additive (MA) processes $ (\xi_n, S_n) $ whose first component satisfies Doeblin's condition and the second one takes valued in $ Z^d $. The derivation is based on a certain perturbation argument that has been used in previous works in the same context. In our asymptotic expansions, however, not only the principal term but also the second order term are expressed explicitly in terms of a few basic functions that are characteristics of the expansion. The second order term will be important for instance in computation of the harmonic measures of a half space for certain models. We introduce a certain aperiodicity condition, named Condition (AP), that seems a minimal one under which the Fourier analysis can be applied straightforwardly. In the case when Condition (AP) is violated the structure of MA processes will be clarified and it will be shown that in a simple manner the process, if not degenerate, are transformed to another one that satisfies Condition (AP) so that from it we derive either directly or indirectly (depending on purpose) the asymptotic expansions for the original process. It in particular is shown that if the MA processes is irreducible as a Markov process, then the Green function is expanded quite similarly to that of a classical random walk on $ Z^d $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "asymptotic expansion, harmonic analysis, semi-Markov process, random walk with internal states, perturbation, aperiodicity, ergodic, Doeblin's condition", } @Article{Pipiras:2007:IRP, author = "Vladas Pipiras and Murad Taqqu", title = "Integral representations of periodic and cyclic fractional stable motions", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "7:181--7:206", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-395", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/395", abstract = "Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their integral representations and show that the periodic fractional stable motions have, in fact, a canonical representation. We study several examples and discuss questions of uniqueness, namely how to determine whether two given integral representations of periodic or cyclic fractional stable motions give rise to the same process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stable, self-similar processes with stationary increments, mixed moving averages, periodic and cyclic flows, cocycles, semi-additive functionals", } @Article{Coquet:2007:CVO, author = "Fran{\c{c}}ois Coquet and Sandrine Toldo", title = "Convergence of values in optimal stopping and convergence of optimal stopping times", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "8:207--8:228", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-288", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/288", abstract = "Under the hypothesis of convergence in probability of a sequence of c{\`a}dl{\`a}g processes $ (X^n) $ to a c{\`a}dl{\`a}g process $X$, we are interested in the convergence of corresponding values in optimal stopping and also in the convergence of optimal stopping times. We give results under hypothesis of inclusion of filtrations or convergence of filtrations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Convergence of filtrations; Convergence of stochastic processes; Convergence of stopping times.; Optimal stopping times; Values in optimal stopping", } @Article{Labarbe:2007:ABR, author = "Jean-Maxime Labarbe and Jean-Fran{\c{c}}ois Marckert", title = "Asymptotics of {Bernoulli} random walks, bridges, excursions and meanders with a given number of peaks", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "9:229--9:261", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-397", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/397", abstract = "A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being +1 or -1, equally likely. The other families quoted in the title are Bernoulli random walks under various conditions. A peak in a trajectory is a local maximum. In this paper, we condition the families of trajectories to have a given number of peaks. We show that, asymptotically, the main effect of setting the number of peaks is to change the order of magnitude of the trajectories. The counting process of the peaks, that encodes the repartition of the peaks in the trajectories, is also studied. It is shown that suitably normalized, it converges to a Brownian bridge which is independent of the limiting trajectory. Applications in terms of plane trees and parallelogram polyominoes are provided, as well as an application to the ``comparison'' between runs and Kolmogorov--Smirnov statistics.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bernoulli random walks; bridge; Brownian meander; excursion; peaks; Weak convergence", } @Article{Ganapathy:2007:RM, author = "Murali Ganapathy", title = "Robust Mixing", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "10:262--10:299", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-398", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/398", abstract = "In this paper, we develop a new ``robust mixing'' framework for reasoning about adversarially modified Markov Chains (AMMC). Let $ \mathbb {P} $ be the transition matrix of an irreducible Markov Chain with stationary distribution $ \pi $. An adversary announces a sequence of stochastic matrices $ \{ \mathbb {A}_t \}_{t > 0} $ satisfying $ \pi \mathbb {A}_t = \pi $. An AMMC process involves an application of $ \mathbb {P} $ followed by $ \mathbb {A}_t $ at time $t$. The robust mixing time of an ergodic Markov Chain $ \mathbb {P}$ is the supremum over all adversarial strategies of the mixing time of the corresponding AMMC process. Applications include estimating the mixing times for certain non-Markovian processes and for reversible liftings of Markov Chains.\par {\bf Non-Markovian card shuffling processes}: The random-to-cyclic transposition process is a {\em non-Markovian} card shuffling process, which at time $t$, exchanges the card at position $ L_t := t {\pmod n}$ with a random card. Mossel, Peres and Sinclair (2004) showed a lower bound of $ (0.0345 + o(1))n \log n$ for the mixing time of the random-to-cyclic transposition process. They also considered a generalization of this process where the choice of $ L_t$ is adversarial, and proved an upper bound of $ C n \log n + O(n)$ (with $ C \approx 4 \times 10^5$) on the mixing time. We reduce the constant to $1$ by showing that the random-to-top transposition chain ({\em a Markov Chain}) has robust mixing time $ \leq n \log n + O(n)$ when the adversarial strategies are limited to holomorphic strategies, i.e., those strategies which preserve the symmetry of the underlying Markov Chain. We also show a $ O(n \log^2 n)$ bound on the robust mixing time of the lazy random-to-top transposition chain when the adversary is not limited to holomorphic strategies.\par {\bf Reversible liftings}: Chen, Lovasz and Pak showed that for a reversible ergodic Markov Chain $ \mathbb {P}$, any reversible lifting $ \mathbb {Q}$ of $ \mathbb {P}$ must satisfy $ \mathcal {T}(\mathbb {P}) \leq \mathcal {T}(\mathbb {Q}) \log (1 / \pi_*)$ where $ \pi_*$ is the minimum stationary probability. Looking at a specific adversarial strategy allows us to show that $ \mathcal {T}(\mathbb {Q}) \geq r(\mathbb {P})$ where $ r(\mathbb {P})$ is the relaxation time of $ \mathbb {P}$. This gives an alternate proof of the reversible lifting result and helps identify cases where reversible liftings cannot improve the mixing time by more than a constant factor.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov Chains, Robust mixing time, Reversible lifting, random-to-cyclic transposition, non-Markovian processes", } @Article{Lachal:2007:FHT, author = "Aim{\'e} Lachal", title = "First Hitting Time and Place, Monopoles and Multipoles for Pseudo-Processes Driven by the Equation {$ \partial u / \partial t = \pm \partial^N u / \partial x^N $}", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "11:300--11:353", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-399", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/399", abstract = "Consider the high-order heat-type equation $ \partial u / \partial t = \pm \partial^N u / \partial x^N $ for an integer $ N > 2 $ and introduce the related Markov pseudo-process $ (X(t))_{t \ge 0} $. In this paper, we study several functionals related to $ (X(t))_{t \ge 0} $: the maximum $ M(t) $ and minimum $ m(t) $ up to time $t$; the hitting times $ \tau_a^+$ and $ \tau_a^-$ of the half lines $ (a, + \infty)$ and $ ( - \infty, a)$ respectively. We provide explicit expressions for the distributions of the vectors $ (X(t), M(t))$ and $ (X(t), m(t))$, as well as those of the vectors $ (\tau_a^+, X(\tau_a^+))$ and $ (\tau_a^-, X(\tau_a^-))$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "first hitting time and place; joint distribution of the process and its maximum/minimum; Multipoles; pseudo-process; Spitzer's identity", } @Article{Valle:2007:EIT, author = "Glauco Valle", title = "Evolution of the interfaces in a two dimensional {Potts} model", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "12:354--12:386", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-346", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/346", abstract = "We investigate the evolution of the random interfaces in a two dimensional Potts model at zero temperature under Glauber dynamics for some particular initial conditions. We prove that under space-time diffusive scaling the shape of the interfaces converges in probability to the solution of a non-linear parabolic equation. This Law of Large Numbers is obtained from the Hydrodynamic limit of a coupling between an exclusion process and an inhomogeneous one dimensional zero range process with asymmetry at the origin.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Exclusion Processes, Interface Dynamics, Hydrodynamic limit", } @Article{Masiero:2007:RPT, author = "Federica Masiero", title = "Regularizing Properties for Transition Semigroups and Semilinear Parabolic Equations in {Banach} Spaces", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "13:387--13:419", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-401", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/401", abstract = "We study regularizing properties for transition semigroups related to Ornstein Uhlenbeck processes with values in a Banach space $E$ which is continuously and densely embedded in a real and separable Hilbert space $H$. Namely we study conditions under which the transition semigroup maps continuous and bounded functions into differentiable functions. Via a Girsanov type theorem such properties extend to perturbed Ornstein Uhlenbeck processes. We apply the results to solve in mild sense semilinear versions of Kolmogorov equations in $E$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Banach spaces.; Ornstein--Uhlenbeck and perturbed Ornstein--Uhlenbeck transition semigroups; parabolic equations; regularizing properties", } @Article{Lambert:2007:QSD, author = "Amaury Lambert", title = "Quasi-Stationary Distributions and the Continuous-State Branching Process Conditioned to Be Never Extinct", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "14:420--14:446", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-402", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/402", abstract = "We consider continuous-state branching (CB) processes which become extinct (i.e., hit 0) with positive probability. We characterize all the quasi-stationary distributions (QSD) for the CB-process as a stochastically monotone family indexed by a real number. We prove that the minimal element of this family is the so-called Yaglom quasi-stationary distribution, that is, the limit of one-dimensional marginals conditioned on being nonzero. Next, we consider the branching process conditioned on not being extinct in the distant future, or $Q$-process, defined by means of Doob $h$-transforms. We show that the $Q$-process is distributed as the initial CB-process with independent immigration, and that under the $ L \log L$ condition, it has a limiting law which is the size-biased Yaglom distribution (of the CB-process). More generally, we prove that for a wide class of nonnegative Markov processes absorbed at 0 with probability 1, the Yaglom distribution is always stochastically dominated by the stationary probability of the $Q$-process, assuming that both exist. Finally, in the diffusion case and in the stable case, the $Q$-process solves a SDE with a drift term that can be seen as the instantaneous immigration.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Continuous-state branching process; h-transform; immigration; L{\'e}vy process; Q-process; quasi-stationary distribution; size-biased distribution; stochastic differential equations; Yaglom theorem", } @Article{Giovanni:2007:SCG, author = "Peccati Giovanni and Murad Taqqu", title = "Stable convergence of generalized {$ L^2 $} stochastic integrals and the principle of conditioning", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "15:447--15:480", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-404", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/404", abstract = "We consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments, and use a decoupling technique, formulated as a \flqq principle of conditioning\frqq, to study their stable convergence towards mixtures of infinitely divisible distributions. The goal of this paper is to develop the theory. Our results apply, in particular, to Skorohod integrals on abstract Wiener spaces, and to multiple integrals with respect to independently scattered and finite variance random measures. The first application is discussed in some detail in the final section of the present work, and further extended in a companion paper (Peccati and Taqqu (2006b)). Applications to the stable convergence (in particular, central limit theorems) of multiple Wiener--It{\^o} integrals with respect to independently scattered (and not necessarily Gaussian) random measures are developed in Peccati and Taqqu (2006a, 2007). The present work concludes with an example involving quadratic Brownian functionals.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Decoupling; Generalized stochastic integrals; Independently scattered measures; multiple Poisson integrals; Principle of conditioning; Resolutions of the identity; Skorohod integrals; Stable convergence; Weak convergence", } @Article{Galvin:2007:SCR, author = "David Galvin", title = "Sampling $3$-colourings of regular bipartite graphs", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "16:481--16:497", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-403", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/403", abstract = "We show that if $ G = (V, E) $ is a regular bipartite graph for which the expansion of subsets of a single parity of $V$ is reasonably good and which satisfies a certain local condition (that the union of the neighbourhoods of adjacent vertices does not contain too many pairwise non-adjacent vertices), and if $M$ is a Markov chain on the set of proper 3-colourings of $G$ which updates the colour of at most $ c|V|$ vertices at each step and whose stationary distribution is uniform, then for $ c < .22$ and $d$ sufficiently large the convergence to stationarity of $M$ is (essentially) exponential in $ |V|$. In particular, if $G$ is the $d$-dimensional hypercube $ Q_d$ (the graph on vertex set $ \{ 0, 1 \}^d$ in which two strings are adjacent if they differ on exactly one coordinate) then the convergence to stationarity of the well-known Glauber (single-site update) dynamics is exponentially slow in $ 2^d / (\sqrt {d} \log d)$. A combinatorial corollary of our main result is that in a uniform 3-colouring of $ Q_d$ there is an exponentially small probability (in $ 2^d$) that there is a colour $i$ such the proportion of vertices of the even subcube coloured $i$ differs from the proportion of the odd subcube coloured $i$ by at most $ .22$. Our proof combines a conductance argument with combinatorial enumeration methods.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Mixing time, 3-colouring, Potts model, conductance, Glauber dynamics, discrete hypercube", } @Article{Evans:2007:ECE, author = "Steven Evans and Tye Lidman", title = "Expectation, Conditional Expectation and Martingales in Local Fields", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "17:498--17:515", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-405", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/405", abstract = "We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy with the observation that for real-valued random variables in $ L^2$ the expected value is the orthogonal projection onto the constants. Previous work has shown that the local field version of $ L^\infty $ is the appropriate counterpart of $ L^2$, and so the expected value of a local field-valued random variable is defined to be its ``projection'' in $ L^\infty $ onto the constants.\par Unlike the real case, the resulting projection is not typically a single constant, but rather a ball in the metric on the local field. However, many properties of this expectation operation and the corresponding conditional expectation mirror those familiar from the real-valued case; for example, conditional expectation is, in a suitable sense, a contraction on $ L^\infty $ and the tower property holds. We also define the corresponding notion of martingale, show that several standard examples of martingales (for example, sums or products of suitable independent random variables or ``harmonic'' functions composed with Markov chains) have local field analogues, and obtain versions of the optional sampling and martingale convergence theorems.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "conditional expectation; expectation; local field; martingale; martingale convergence; optional sampling; projection", } @Article{Gartner:2007:ICS, author = "J{\"u}rgen G{\"a}rtner and Frank den Hollander and Gregory Maillard", title = "Intermittency on catalysts: symmetric exclusion", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "18:516--18:573", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-407", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/407", abstract = "We continue our study of intermittency for the parabolic Anderson equation, i.e., the spatially discrete heat equation on the d-dimensional integer lattice with a space-time random potential. The solution of the equation describes the evolution of a ``reactant'' under the influence of a ``catalyst''. In this paper we focus on the case where the random field is an exclusion process with a symmetric random walk transition kernel, starting from Bernoulli equilibrium. We consider the annealed Lyapunov exponents, i.e., the exponential growth rates of the successive moments of the solution. We show that these exponents are trivial when the random walk is recurrent, but display an interesting dependence on the diffusion constant when the random walk is transient, with qualitatively different behavior in different dimensions. Special attention is given to the asymptotics of the exponents when the diffusion constant tends to infinity, which is controlled by moderate deviations of the random field requiring a delicate expansion argument.\par In G{\"a}rtner and den Hollander [10] the case of a Poisson field of independent (simple) random walks was studied. The two cases show interesting differences and similarities. Throughout the paper, a comparison of the two cases plays a crucial role.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "catalytic random medium; exclusion processes; intermittency; Lyapunov exponents; Parabolic Anderson model", } @Article{Warren:2007:DBM, author = "Jon Warren", title = "{Dyson}'s {Brownian} motions, intertwining and interlacing", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "19:573--19:590", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-406", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/406", abstract = "A reflected Brownian motion in the Gelfand--Tsetlin cone is used to construct Dyson's process of non-colliding Brownian motions. The key step of the construction is to consider two interlaced families of Brownian paths with paths belonging to the second family reflected off paths belonging to the first. Such families of paths are known to arise in the Arratia flow of coalescing Brownian motions. A determinantal formula for the distribution of coalescing Brownian motions is presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coalescing Brownian motions; Gelfand--Tsetlin cone.; intertwining; non-colliding Brownian motions", } @Article{Benjamini:2007:RSR, author = "Itai Benjamini and Roey Izkovsky and Harry Kesten", title = "On the Range of the Simple Random Walk Bridge on Groups", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "20:591--20:612", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-408", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/408", abstract = "Let $G$ be a vertex transitive graph. A study of the range of simple random walk on $G$ and of its bridge is proposed. While it is expected that on a graph of polynomial growth the sizes of the range of the unrestricted random walk and of its bridge are the same in first order, this is not the case on some larger graphs such as regular trees. Of particular interest is the case when $G$ is the Cayley graph of a group. In this case we even study the range of a general symmetric (not necessarily simple) random walk on $G$. We hope that the few examples for which we calculate the first order behavior of the range here will help to discover some relation between the group structure and the behavior of the range. Further problems regarding bridges are presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "range of a bridge; range of random walk", } @Article{Toninelli:2007:CLR, author = "Fabio Lucio Toninelli", title = "Correlation Lengths for Random Polymer Models and for Some Renewal Sequences", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "21:613--21:636", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-414", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/414", abstract = "We consider models of directed polymers interacting with a one-dimensional defect line on which random charges are placed. More abstractly, one starts from renewal sequence on $Z$ and gives a random (site-dependent) reward or penalty to the occurrence of a renewal at any given point of $Z$. These models are known to undergo a delocalization-localization transition, and the free energy $F$ vanishes when the critical point is approached from the localized region. We prove that the quenched correlation length $ \xi $, defined as the inverse of the rate of exponential decay of the two-point function, does not diverge faster than $ 1 / F$. We prove also an exponentially decaying upper bound for the disorder-averaged two-point function, with a good control of the sub-exponential prefactor. We discuss how, in the particular case where disorder is absent, this result can be seen as a refinement of the classical renewal theorem, for a specific class of renewal sequences.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Pinning and Wetting Models, Typical and Average Correlation Lengths, Critical Exponents, Renewal Theory, Exponential Convergence Rates", } @Article{Matzinger:2007:DLP, author = "Heinrich Matzinger and Serguei Popov", title = "Detecting a Local Perturbation in a Continuous Scenery", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "22:637--22:660", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-409", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/409", abstract = "A continuous one-dimensional scenery is a double-infinite sequence of points (thought of as locations of {\em bells}) in $R$. Assume that a scenery $X$ is observed along the path of a Brownian motion in the following way: when the Brownian motion encounters a bell different from the last one visited, we hear a ring. The trajectory of the Brownian motion is unknown, whilst the scenery $X$ is known except in some finite interval. We prove that given only the sequence of times of rings, we can a.s. reconstruct the scenery $X$ entirely. For this we take the scenery$X$ to be a local perturbation of a Poisson scenery $ X'$. We present an explicit reconstruction algorithm. This problem is the continuous analog of the ``detection of a defect in a discrete scenery''. Many of the essential techniques used with discrete sceneries do not work with continuous sceneries.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, Poisson process, localization test, detecting defects in sceneries seen along random walks", } @Article{Dietz:2007:OLS, author = "Zach Dietz and Sunder Sethuraman", title = "Occupation laws for some time-nonhomogeneous {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "23:661--23:683", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-413", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/413", abstract = "We consider finite-state time-nonhomogeneous Markov chains whose transition matrix at time $n$ is $ I + G / n^z$ where $G$ is a ``generator'' matrix, that is $ G(i, j) > 0$ for $ i, j$ distinct, and $ G(i, i) = - \sum_{k \ne i} G(i, k)$, and $ z > 0$ is a strength parameter. In these chains, as time grows, the positions are less and less likely to change, and so form simple models of age-dependent time-reinforcing schemes. These chains, however, exhibit a trichotomy of occupation behaviors depending on parameters.\par We show that the average occupation or empirical distribution vector up to time $n$, when variously $ 0 < z < 1$, $ z > 1$ or $ z = 1$, converges in probability to a unique ``stationary'' vector $ n_G$, converges in law to a nontrivial mixture of point measures, or converges in law to a distribution $ m_G$ with no atoms and full support on a simplex respectively, as $n$ tends to infinity. This last type of limit can be interpreted as a sort of ``spreading'' between the cases $ 0 < z < 1$ and $ z > 1$.\par In particular, when $G$ is appropriately chosen, $ m_G$ is a Dirichlet distribution, reminiscent of results in Polya urns.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "laws of large numbers, nonhomogeneous, Markov, occupation, reinforcement, Dirichlet distribution", } @Article{Ferrari:2007:QSD, author = "Pablo Ferrari and Nevena Maric", title = "Quasi Stationary Distributions and {Fleming--Viot} Processes in Countable Spaces", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "24:684--24:702", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-415", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/415", abstract = "We consider an irreducible pure jump Markov process with rates $ Q = (q(x, y)) $ on $ \Lambda \cup \{ 0 \} $ with $ \Lambda $ countable and $0$ an absorbing state. A {\em quasi stationary distribution \rm} (QSD) is a probability measure $ \nu $ on $ \Lambda $ that satisfies: starting with $ \nu $, the conditional distribution at time $t$, given that at time $t$ the process has not been absorbed, is still $ \nu $. That is, $ \nu (x) = \nu P_t(x) / (\sum_{y \in \Lambda } \nu P_t(y))$, with $ P_t$ the transition probabilities for the process with rates $Q$.\par A {\em Fleming--Viot} (FV) process is a system of $N$ particles moving in $ \Lambda $. Each particle moves independently with rates $Q$ until it hits the absorbing state $0$; but then instantaneously chooses one of the $ N - 1$ particles remaining in $ \Lambda $ and jumps to its position. Between absorptions each particle moves with rates $Q$ independently.\par Under the condition $ \alpha := \sum_{x \in \Lambda } \inf Q(\cdot, x) > \sup Q(\cdot, 0) := C$ we prove existence of QSD for $Q$; uniqueness has been proven by Jacka and Roberts. When $ \alpha > 0$ the FV process is ergodic for each $N$. Under $ \alpha > C$ the mean normalized densities of the FV unique stationary measure converge to the QSD of $Q$, as $ N \to \infty $; in this limit the variances vanish.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Fleming--Viot process; Quasi stationary distributions", } @Article{vanderHofstad:2007:DRG, author = "Remco van der Hofstad and Gerard Hooghiemstra and Dmitri Znamenski", title = "Distances in Random Graphs with Finite Mean and Infinite Variance Degrees", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "25:703--25:766", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-420", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/420", abstract = "In this paper we study typical distances in random graphs with i.i.d. degrees of which the tail of the common distribution function is regularly varying with exponent $ 1 - \tau $. Depending on the value of the parameter $ \tau $ we can distinct three cases: (i) $ \tau > 3 $, where the degrees have finite variance, (ii) $ \tau \in (2, 3) $, where the degrees have infinite variance, but finite mean, and (iii) $ \tau \in (1, 2) $, where the degrees have infinite mean. The distances between two randomly chosen nodes belonging to the same connected component, for $ \tau > 3 $ and $ \tau \in (1, 2), $ have been studied in previous publications, and we survey these results here. When $ \tau \in (2, 3) $, the graph distance centers around $ 2 \log \log {N} / | \log (\tau - 2)| $. We present a full proof of this result, and study the fluctuations around this asymptotic means, by describing the asymptotic distribution. The results presented here improve upon results of Reittu and Norros, who prove an upper bound only.\par The random graphs studied here can serve as models for complex networks where degree power laws are observed; this is illustrated by comparing the typical distance in this model to Internet data, where a degree power law with exponent $ \tau \approx 2.2 $ is observed for the so-called Autonomous Systems (AS) graph", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching processes, configuration model, coupling, graph distance", } @Article{Gnedin:2007:CR, author = "Alexander Gnedin", title = "The Chain Records", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "26:767--26:786", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-410", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/410", abstract = "Chain records is a new type of multidimensional record. We discuss how often the chain records occur when the background sampling is from the unit cube with uniform distribution (or, more generally, from an arbitrary continuous product distribution in d dimensions). Extensions are given for sampling from more general spaces with a self-similarity property.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "chains; Ewens partition; multidimensional records; random orders", } @Article{Feng:2007:LDD, author = "Shui Feng", title = "Large Deviations for {Dirichlet} Processes and {Poisson--Dirichlet} Distribution with Two Parameters", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "27:787--27:807", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-417", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/417", abstract = "Large deviation principles are established for the two-parameter Poisson--Dirichlet distribution and two-parameter Dirichlet process when parameter $ \theta $ approaches infinity. The motivation for these results is to understand the differences in terms of large deviations between the two-parameter models and their one-parameter counterparts. New insight is obtained about the role of the second parameter $ \alpha $ through a comparison with the corresponding results for the one-parameter Poisson--Dirichlet distribution and Dirichlet process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dirichlet processes; GEM representation; large deviations; Poisson--Dirichlet distribution", } @Article{Taylor:2007:CAP, author = "Jesse Taylor", title = "The Common Ancestor Process for a {Wright--Fisher} Diffusion", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "28:808--28:847", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-418", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/418", abstract = "Rates of molecular evolution along phylogenetic trees are influenced by mutation, selection and genetic drift. Provided that the branches of the tree correspond to lineages belonging to genetically isolated populations (e.g., multi-species phylogenies), the interplay between these three processes can be described by analyzing the process of substitutions to the common ancestor of each population. We characterize this process for a class of diffusion models from population genetics theory using the structured coalescent process introduced by Kaplan et al. (1988) and formalized in Barton et al. (2004). For two-allele models, this approach allows both the stationary distribution of the type of the common ancestor and the generator of the common ancestor process to be determined by solving a one-dimensional boundary value problem. In the case of a Wright--Fisher diffusion with genic selection, this solution can be found in closed form, and we show that our results complement those obtained by Fearnhead (2002) using the ancestral selection graph. We also observe that approximations which neglect recurrent mutation can significantly underestimate the exact substitution rates when selection is strong. Furthermore, although we are unable to find closed-form expressions for models with frequency-dependent selection, we can still solve the corresponding boundary value problem numerically and then use this solution to calculate the substitution rates to the common ancestor. We illustrate this approach by studying the effect of dominance on the common ancestor process in a diploid population. Finally, we show that the theory can be formally extended to diffusion models with more than two genetic backgrounds, but that it leads to systems of singular partial differential equations which we have been unable to solve.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Common-ancestor process; diffusion process; genetic drift; selection; structured coalescent; substitution rates", } @Article{Gautier:2007:SNS, author = "Eric Gautier", title = "Stochastic Nonlinear {Schr{\"o}dinger} Equations Driven by a Fractional Noise. {Well}-Posedness, Large Deviations and Support", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "29:848--29:861", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-416", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/416", abstract = "We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter $ H \in (0, 1) $ and colored in space with a nuclear space correlation operator. We study local well-posedness. Under adequate assumptions on the initial data, the space correlations of the noise and for some saturated nonlinearities, we prove sample path large deviations and support results in a space of Holder continuous in time until blow-up paths. We consider Kerr nonlinearities when $ H > 1 / 2 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractional Brownian motion; Large deviations; nonlinear Schrodinger equation; stochastic partial differential equations", } @Article{Hambly:2007:NVP, author = "Ben Hambly and Liza Jones", title = "Number variance from a probabilistic perspective: infinite systems of independent {Brownian} motions and symmetric alpha stable processes", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "30:862--30:887", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-419", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See erratum \cite{Hambly:2009:ENV}.", URL = "http://ejp.ejpecp.org/article/view/419", abstract = "Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct explicit new examples of processes which exhibit both divergent and saturating number variance behaviour. We derive a general expression for the number variance for the spatial particle configurations arising from these systems and this enables us to deduce various limiting distribution results for the fluctuations of the associated counting functions. In particular, knowledge of the number variance allows us to introduce and characterize a novel family of centered, long memory Gaussian processes. We obtain fractional Brownian motion as a weak limit of these constructed processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "controlled variability; fractional Brownian motion; functional limits; Gaussian fluctuations; Gaussian processes; long memory; Number variance; symmetric alpha-stable processes", } @Article{Weill:2007:ARB, author = "Mathilde Weill", title = "Asymptotics for Rooted Bipartite Planar Maps and Scaling Limits of Two-Type Spatial Trees", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "31:862--31:925", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-425", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/425", abstract = "We prove some asymptotic results for the radius and the profile of large random bipartite planar maps. Using a bijection due to Bouttier, Di Francesco and Guitter between rooted bipartite planar maps and certain two-type trees with positive labels, we derive our results from a conditional limit theorem for two-type spatial trees. Finally we apply our estimates to separating vertices of bipartite planar maps: with probability close to one when n tends to infinity, a random $ 2 k$-angulation with n faces has a separating vertex whose removal disconnects the map into two components each with size greater that $ n^{1 / 2 - \varepsilon }$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Conditioned Brownian snake; Planar maps; two-type Galton--Watson trees", } @Article{Benjamini:2007:RGH, author = "Itai Benjamini and Ariel Yadin and Amir Yehudayoff", title = "Random Graph-Homomorphisms and Logarithmic Degree", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "32:926--32:950", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-427", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/427", abstract = "A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of a uniformly chosen homomorphism from a graph $G$ to the infinite line $Z$. It is shown that if the maximal degree of $G$ is `sub-logarithmic', then the range of such a homomorphism is super-constant.\par Furthermore, some examples are provided, suggesting that perhaps for graphs with super-logarithmic degree, the range of a typical homomorphism is bounded. In particular, a sharp transition is shown for a specific family of graphs $ C_{n, k}$ (which is the tensor product of the $n$-cycle and a complete graph, with self-loops, of size $k$). That is, given any function $ \psi (n)$ tending to infinity, the range of a typical homomorphism of $ C_{n, k}$ is super-constant for $ k = 2 \log (n) - \psi (n)$, and is $3$ for $ k = 2 \log (n) + \psi (n)$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kurtz:2007:YWE, author = "Thomas Kurtz", title = "The {Yamada--Watanabe--Engelbert} theorem for general stochastic equations and inequalities", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "33:951--33:965", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-431", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/431", abstract = "A general version of the Yamada--Watanabe and Engelbert results relating existence and uniqueness of strong and weak solutions for stochastic equations is given. The results apply to a wide variety of stochastic equations including classical stochastic differential equations, stochastic partial differential equations, and equations involving multiple time transformations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "weak solution, strong solution, pathwise uniqueness, stochastic differential equations, stochastic partial differential equations, multidimensional index", } @Article{Major:2007:MVB, author = "Peter Major", title = "On a Multivariate Version of {Bernstein}'s Inequality", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "34:966--34:988", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-430", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/430", abstract = "We prove such a multivariate version of Bernstein's inequality about the tail distribution of degenerate $U$-statistics which is an improvement of some former results. This estimate will be compared with an analogous bound about the tail distribution of multiple Wiener--It{\^o} integrals. Their comparison shows that our estimate is sharp. The proof is based on good estimates about high moments of degenerate $U$-statistics. They are obtained by means of a diagram formula which enables us to express the product of degenerate $U$-statistics as the sum of such expressions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bernstein inequality, (degenerate) U-statistics, Wiener--It{\^o} integrals, diagram formula, moment estimates", } @Article{Penrose:2007:GLR, author = "Mathew Penrose", title = "{Gaussian} Limts for Random Geometric Measures", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "35:989--35:1035", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-429", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/429", abstract = "Given $n$ independent random marked $d$-vectors $ X_i$ with a common density, define the measure $ \nu_n = \sum_i \xi_i $, where $ \xi_i$ is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near $ X_i$. Technically, this means here that $ \xi_i$ stabilizes with a suitable power-law decay of the tail of the radius of stabilization. For bounded test functions $f$ on $ R^d$, we give a central limit theorem for $ \nu_n(f)$, and deduce weak convergence of $ \nu_n(\cdot)$, suitably scaled and centred, to a Gaussian field acting on bounded test functions. The general result is illustrated with applications to measures associated with germ-grain models, random and cooperative sequential adsorption, Voronoi tessellation and $k$-nearest neighbours graph.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random measures", } @Article{Turova:2007:CPT, author = "Tatyana Turova", title = "Continuity of the percolation threshold in randomly grown graphs", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "36:1036--36:1047", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-436", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/436", abstract = "We consider various models of randomly grown graphs. In these models the vertices and the edges accumulate within time according to certain rules. We study a phase transition in these models along a parameter which refers to the mean life-time of an edge. Although deleting old edges in the uniformly grown graph changes abruptly the properties of the model, we show that some of the macro-characteristics of the graph vary continuously. In particular, our results yield a lower bound for the size of the largest connected component of the uniformly grown graph.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching processes; Dynamic random graphs; phase transition", } @Article{Johansson:2007:EEG, author = "Kurt Johansson and Eric Nordenstam", title = "Erratum to {``Eigenvalues of GUE Minors''}", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "37:1048--37:1051", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-816", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Johansson:2006:EGM}.", URL = "http://ejp.ejpecp.org/article/view/816", abstract = "In the paper \url{http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1647}, two expressions for the so called GUE minor kernel are presented, one in definition 1.2 and one in the formulas (5.6) and (5.7). The expressions given in (5.6) and (5.7) are correct, but the expression in definition 1.2 of the paper has to be modified in the case $ r > s $. The proof of the equality of the two expressions for the GUE minor kernel given in the paper was based on lemma 5.6 which is not correct since some terms in the expansion are missing. The correct expansion is given in lemma 1.2 below.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Arias-Castro:2007:IRH, author = "Ery Arias-Castro", title = "Interpolation of Random Hyperplanes", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "38:1052--38:1071", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-435", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/435", abstract = "Let $ \{ (Z_i, W_i) \colon i = 1, \dots, n \} $ be uniformly distributed in $ [0, 1]^d \times \mathbb {G}(k, d) $, where $ \mathbb {G}(k, d) $ denotes the space of $k$-dimensional linear subspaces of $ \mathbb {R}^d$. For a differentiable function $ f \colon [0, 1]^k \rightarrow [0, 1]^d$, we say that $f$ interpolates $ (z, w) \in [0, 1]^d \times \mathbb {G}(k, d)$ if there exists $ x \in [0, 1]^k$ such that $ f(x) = z$ and $ \vec {f}(x) = w$, where $ \vec {f}(x)$ denotes the tangent space at $x$ defined by $f$. For a smoothness class $ {\cal F}$ of Holder type, we obtain probability bounds on the maximum number of points a function $ f \in {\cal F}$ interpolates.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Grassmann Manifold; Haar Measure; Kolmogorov Entropy; Pattern Recognition", } @Article{Bobkov:2007:LDI, author = "Sergey Bobkov", title = "Large deviations and isoperimetry over convex probability measures with heavy tails", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "39:1072--39:1100", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-440", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/440", abstract = "Large deviations and isoperimetric inequalities are considered for probability distributions, satisfying convexity conditions of the Brunn--Minkowski-type", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Large deviations, convex measures, dilation of sets, transportation of mass, Khinchin-type, isoperimetric, weak Poincar{\'e}, Sobolev-type inequalities", } @Article{Griffiths:2007:RIA, author = "Robert Griffiths and Dario Spano", title = "Record Indices and Age-Ordered Frequencies in Exchangeable {Gibbs} Partitions", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "40:1101--40:1130", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-434", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/434", abstract = "The frequencies of an exchangeable Gibbs random partition of the integers (Gnedin and Pitman 2005) are considered in their age-order, i.e., their size-biased order. We study their dependence on the sequence of record indices (i.e., the least elements) of the blocks of the partition. In particular we show that, conditionally on the record indices, the distribution of the age-ordered frequencies has a left-neutral stick-breaking structure. Such a property in fact characterizes the Gibbs family among all exchangeable partitions and leads to further interesting results on: (i) the conditional Mellin transform of the $k$-th oldest frequency given the $k$-th record index, and (ii) the conditional distribution of the first $k$ normalized frequencies, given their sum and the $k$-th record index; the latter turns out to be a mixture of Dirichlet distributions. Many of the mentioned representations are extensions of Griffiths and Lessard (2005) results on Ewens' partitions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Exchangeable Gibbs Partitions, GEM distribution, Age-ordered frequencies, Beta-Stacy distribution, Neutral distributions, Record indices", } @Article{Maida:2007:LDL, author = "Myl{\`e}ne Maida", title = "Large deviations for the largest eigenvalue of rank one deformations of {Gaussian} ensembles", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "41:1131--41:1150", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-438", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/438", abstract = "We establish a large deviation principle for the largest eigenvalue of a rank one deformation of a matrix from the GUE or GOE. As a corollary, we get another proof of the phenomenon, well-known in learning theory and finance, that the largest eigenvalue separates from the bulk when the perturbation is large enough. A large part of the paper is devoted to an auxiliary result on the continuity of spherical integrals in the case when one of the matrix is of rank one, as studied in one of our previous works.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "large deviations; random matrices", } @Article{Evans:2007:AEA, author = "Steven Evans and Tye Lidman", title = "Asymptotic Evolution of Acyclic Random Mappings", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "42:1051--42:1180", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-437", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/437", abstract = "An acyclic mapping from an $n$ element set into itself is a mapping $ \varphi $ such that if $ \varphi^k(x) = x$ for some $k$ and $x$, then $ \varphi (x) = x$. Equivalently, $ \varphi^\ell = \varphi^{\ell + 1} = \ldots $ for $ \ell $ sufficiently large. We investigate the behavior as $ n \rightarrow \infty $ of a sequence of a Markov chain on the collection of such mappings. At each step of the chain, a point in the $n$ element set is chosen uniformly at random and the current mapping is modified by replacing the current image of that point by a new one chosen independently and uniformly at random, conditional on the resulting mapping being again acyclic. We can represent an acyclic mapping as a directed graph (such a graph will be a collection of rooted trees) and think of these directed graphs as metric spaces with some extra structure. Informal calculations indicate that the metric space valued process associated with the Markov chain should, after an appropriate time and ``space'' rescaling, converge as $ n \rightarrow \infty $ to a real tree ($R$-tree) valued Markov process that is reversible with respect to a measure induced naturally by the standard reflected Brownian bridge. Although we don't prove such a limit theorem, we use Dirichlet form methods to construct a Markov process that is Hunt with respect to a suitable Gromov--Hausdorff-like metric and evolves according to the dynamics suggested by the heuristic arguments. This process is similar to one that appears in earlier work by Evans and Winter as a similarly informal limit of a Markov chain related to the subtree prune and regraft tree (SPR) rearrangements from phylogenetics.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian bridge; Brownian excursion; continuum random tree; Dirichlet form; excursion theory; Gromov--Hausdorff metric; path decomposition; random mapping", } @Article{Darses:2007:TRD, author = "Sebastien Darses and Bruno Saussereau", title = "Time Reversal for Drifted Fractional {Brownian} Motion with {Hurst} Index {$ H > 1 / 2 $}", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "43:1181--43:1211", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-439", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/439", abstract = "Let $X$ be a drifted fractional Brownian motion with Hurst index $ H > 1 / 2$. We prove that there exists a fractional backward representation of $X$, i.e., the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when $ H = 1 / 2$. We then apply our result to stochastic differential equations driven by a fractional Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Fractional Brownian motion; Malliavin Calculus.; Time reversal", } @Article{Barthe:2007:IBE, author = "Franck Barthe and Patrick Cattiaux and Cyril Roberto", title = "Isoperimetry between exponential and {Gaussian}", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "44:1212--44:1237", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-441", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/441", abstract = "We study the isoperimetric problem for product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are approximate solutions of the isoperimetric problem", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Isoperimetry; Super-Poincar{\'e} inequality", } @Article{Rider:2007:CDP, author = "Brian Rider and Balint Virag", title = "Complex Determinantal Processes and {$ H1 $} Noise", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "45:1238--45:1257", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-446", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/446", abstract = "For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinantal point processes $ \mathcal Z_\rho $ with intensity $ \rho d \nu $, where $ \nu $ is the corresponding invariant measure. We show that as $ \rho \to \infty $, after centering, these processes converge to invariant $ H^1 $ noise. More precisely, for all functions $ f \in H^1 (\nu) \cap L^1 (\nu) $ the distribution of $ \sum_{z \in \mathcal Z} f(z) - \frac {\rho }{\pi } \int f d \nu $ converges to Gaussian with mean zero and variance $ \frac {1}{4 \pi } \| f \|_{H^1}^2 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "determinantal process; invariant point process; noise limit; random matrices", } @Article{Neunhauserer:2007:RWI, author = "J{\"o}rg Neunh{\"a}userer", title = "Random walks on infinite self-similar graphs", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "46:1258--46:1275", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-448", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/448", abstract = "We introduce a class of rooted infinite self-similar graphs containing the well known Fibonacci graph and graphs associated with Pisot numbers. We consider directed random walks on these graphs and study their entropy and their limit measures. We prove that every infinite self-similar graph has a random walk of full entropy and that the limit measures of this random walks are absolutely continuous.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "graph; random walk", } @Article{Klass:2007:UAQ, author = "Michael Klass and Krzysztof Nowicki", title = "Uniformly Accurate Quantile Bounds Via The Truncated Moment Generating Function: The Symmetric Case", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "47:1276--47:1298", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-452", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/452", abstract = "Let $ X_1, X_2, \dots $ be independent and symmetric random variables such that $ S_n = X_1 + \cdots + X_n $ converges to a finite valued random variable $S$ a.s. and let $ S^* = \sup_{1 \leq n \leq \infty } S_n$ (which is finite a.s.). We construct upper and lower bounds for $ s_y$ and $ s_y^*$, the upper $ 1 / y$-th quantile of $ S_y$ and $ S^*$, respectively. Our approximations rely on an explicitly computable quantity $ \underline q_y$ for which we prove that\par $$ \frac 1 2 \underline q_{y / 2} < s_y^* < 2 \underline q_{2y} \quad \text { and } \quad \frac 1 2 \underline q_{ (y / 4) (1 + \sqrt { 1 - 8 / y})} < s_y < 2 \underline q_{2y}. $$ The RHS's hold for $ y \geq 2$ and the LHS's for $ y \geq 94$ and $ y \geq 97$, respectively. Although our results are derived primarily for symmetric random variables, they apply to non-negative variates and extend to an absolute value of a sum of independent but otherwise arbitrary random variables.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Sum of independent rv's, tail distributions, tail distributions, tail probabilities, quantile approximation, Hoffmann--J{\o}rgensen/Klass--Nowicki Inequality", } @Article{Grigorescu:2007:EPM, author = "Ilie Grigorescu and Min Kang", title = "Ergodic Properties of Multidimensional {Brownian} Motion with Rebirth", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "48:1299--48:1322", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-450", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/450", abstract = "In a bounded open region of the $d$ dimensional space we consider a Brownian motion which is reborn at a fixed interior point as soon as it reaches the boundary. The evolution is invariant with respect to a density equal, modulo a constant, to the Green function of the Dirichlet Laplacian centered at the point of return. We calculate the resolvent in closed form, study its spectral properties and determine explicitly the spectrum in dimension one. Two proofs of the exponential ergodicity are given, one using the inverse Laplace transform and properties of analytic semigroups, and the other based on Doeblin's condition. Both methods admit generalizations to a wide class of processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dirichlet Laplacian, Green function, analytic semigroup, jump diffusion", } @Article{Biskup:2007:FCR, author = "Marek Biskup and Timothy Prescott", title = "Functional {CLT} for Random Walk Among Bounded Random Conductances", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "49:1323--49:1348", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-456", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/456", abstract = "We consider the nearest-neighbor simple random walk on $ Z^d $, $ d \ge 2 $, driven by a field of i.i.d. random nearest-neighbor conductances $ \omega_{xy} \in [0, 1] $. Apart from the requirement that the bonds with positive conductances percolate, we pose no restriction on the law of the $ \omega $'s. We prove that, for a.e. realization of the environment, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. The quenched functional CLT holds despite the fact that the local CLT may fail in $ d \ge 5 $ due to anomalously slow decay of the probability that the walk returns to the starting point at a given time.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random conductance model, invariance principle, corrector, homogenization, heat kernel, percolation, isoperimetry", } @Article{Mytnik:2007:LES, author = "Leonid Mytnik and Jie Xiong", title = "Local extinction for superprocesses in random environments", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "50:1349--50:1378", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-457", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/457", abstract = "We consider a superprocess in a random environment represented by a random measure which is white in time and colored in space with correlation kernel $ g(x, y) $. Suppose that $ g(x, y) $ decays at a rate of $ |x - y|^{- \alpha } $, $ 0 \leq \alpha \leq 2 $, as $ |x - y| \to \infty $. We show that the process, starting from Lebesgue measure, suffers long-term local extinction. If $ \alpha < 2 $, then it even suffers finite time local extinction. This property is in contrast with the classical super-Brownian motion which has a non-trivial limit when the spatial dimension is higher than 2. We also show in this paper that in dimensions $ d = 1, 2 $ superprocess in random environment suffers local extinction for any bounded function $g$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Tykesson:2007:NUC, author = "Johan Tykesson", title = "The number of unbounded components in the {Poisson} {Boolean} model of continuum percolation in hyperbolic space", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "51:1379--51:1401", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-460", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/460", abstract = "We consider the Poisson Boolean model of continuum percolation with balls of fixed radius $R$ in $n$-dimensional hyperbolic space $ H^n$. Let $ \lambda $ be the intensity of the underlying Poisson process, and let $ N_C$ denote the number of unbounded components in the covered region. For the model in any dimension we show that there are intensities such that $ N_C = \infty $ a.s. if $R$ is big enough. In $ H^2$ we show a stronger result: for any $R$ there are two intensities $ \lambda_c$ and $ \lambda_u$ where $ 0 < \lambda_c < \lambda_u < \infty $, such that$ N_C = 0$ for $ \lambda \in [0, \lambda_c]$, $ N_C = \infty $ for $ \lambda \in (\lambda_c, \lambda_u)$ and $ N_C = 1$ for $ \lambda \in [\lambda_u, \infty)$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "continuum percolation; hyperbolic space; phase transitions", } @Article{Hu:2007:EES, author = "Zhishui Hu and John Robinson and Qiying Wang", title = "{Edgeworth} Expansions for a Sample Sum from a Finite Set of Independent Random Variables", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "52:1402--52:1417", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-447", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/447", abstract = "Let $ \{ X_1, \cdots, X_N \} $ be a set of $N$ independent random variables, and let $ S_n$ be a sum of $n$ random variables chosen without replacement from the set $ \{ X_1, \cdots, X_N \} $ with equal probabilities. In this paper we give a one-term Edgeworth expansion of the remainder term for the normal approximation of $ S_n$ under mild conditions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Edgeworth expansion, finite population, sampling without replacement", } @Article{Ankirchner:2007:CVD, author = "Stefan Ankirchner and Peter Imkeller and Goncalo {Dos Reis}", title = "Classical and Variational Differentiability of {BSDEs} with Quadratic Growth", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "53:1418--53:1453", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-462", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/462", abstract = "We consider Backward Stochastic Differential Equations (BSDEs) with generators that grow quadratically in the control variable. In a more abstract setting, we first allow both the terminal condition and the generator to depend on a vector parameter $x$. We give sufficient conditions for the solution pair of the BSDE to be differentiable in $x$. These results can be applied to systems of forward--backward SDE. If the terminal condition of the BSDE is given by a sufficiently smooth function of the terminal value of a forward SDE, then its solution pair is differentiable with respect to the initial vector of the forward equation. Finally we prove sufficient conditions for solutions of quadratic BSDEs to be differentiable in the variational sense (Malliavin differentiable).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "BSDE, forward--backward SDE, quadratic growth, differentiability, stochastic calculus of variations, Malliavin calculus, Feynman--Kac formula, BMO martingale, reverse Holder inequality", } @Article{Aldous:2007:PUR, author = "David Aldous and Russell Lyons", title = "Processes on Unimodular Random Networks", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "54:1454--54:1508", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-463", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See errata \cite{Aldous:2017:EPU,Aldous:2019:SEP}.", URL = "http://ejp.ejpecp.org/article/view/463", abstract = "We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning random walks, percolation, spanning forests, and amenability from the known context of unimodular quasi-transitive graphs to the more general context of unimodular random networks. We give properties of a trace associated to unimodular random networks with applications to stochastic comparison of continuous-time random walk.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Amenability, equivalence relations, infinite graphs, percolation, quasi-transitive, random walks, transitivity, weak convergence, reversibility, trace, stochastic comparison, spanning forests, sofic groups", } @Article{White:2007:PID, author = "David White", title = "Processes with inert drift", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "55:1509--55:1546", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-465", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/465", abstract = "We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in a paper by Knight [7]. We construct and give asymptotic results for two different arrangements of inert particles and Brownian particles, and construct the analogous process in higher dimensions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; local time; Skorohod lemma", } @Article{Gnedin:2007:NCL, author = "Alexander Gnedin and Yuri Yakubovich", title = "On the Number of Collisions in Lambda-Coalescents", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "56:1547--56:1567", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-464", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/464", abstract = "We examine the total number of collisions $ C_n $ in the $ \Lambda $-coalescent process which starts with $n$ particles. A linear growth and a stable limit law for $ C_n$ are shown under the assumption of a power-like behaviour of the measure $ \Lambda $ near $0$ with exponent $ 0 < \alpha < 1$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "collisions; Lambda-coalescent; stable limit", } @Article{Feng:2007:GIF, author = "Chunrong Feng and Huaizhong Zhao", title = "A Generalized {It{\^o}}'s Formula in Two-Dimensions and Stochastic {Lebesgue--Stieltjes} Integrals", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "57:1568--57:1599", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-468", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/468", abstract = "In this paper, a generalized It$ {\hat {\rm o}} $'s formula for continuous functions of two-dimensional continuous semimartingales is proved. The formula uses the local time of each coordinate process of the semimartingale, the left space first derivatives and the second derivative $ \nabla_1^- \nabla_2^-f $, and the stochastic Lebesgue--Stieltjes integrals of two parameters. The second derivative $ \nabla_1^- \nabla_2^-f $ is only assumed to be of locally bounded variation in certain variables. Integration by parts formulae are asserted for the integrals of local times. The two-parameter integral is defined as a natural generalization of both the It{\^o} integral and the Lebesgue--Stieltjes integral through a type of It$ {\hat {\rm o }} $ isometry formula.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "continuous semimartingale; generalized It{\^o}'s formula; local time; stochastic Lebesgue--Stieltjes integral", } @Article{Janson:2007:TEB, author = "Svante Janson and Guy Louchard", title = "Tail estimates for the {Brownian} excursion area and other {Brownian} areas", journal = j-ELECTRON-J-PROBAB, volume = "12", pages = "58:1600--58:1632", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v12-471", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/471", abstract = "Brownian areas are considered in this paper: the Brownian excursion area, the Brownian bridge area, the Brownian motion area, the Brownian meander area, the Brownian double meander area, the positive part of Brownian bridge area, the positive part of Brownian motion area. We are interested in the asymptotics of the right tail of their density function. Inverting a double Laplace transform, we can derive, in a mechanical way, all terms of an asymptotic expansion. We illustrate our technique with the computation of the first four terms. We also obtain asymptotics for the right tail of the distribution function and for the moments. Our main tool is the two-dimensional saddle point method.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian areas, asymptotics for density functions right tail, double Laplace transform, two-dimensional saddle point method", } @Article{Chaumont:2008:CLP, author = "Lo{\"\i}c Chaumont and Ronald Doney", title = "Corrections to {``On L{\'e}vy processes conditioned to stay positive''}", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "1:1--1:4", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-466", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Chaumont:2005:LPC}.", URL = "http://ejp.ejpecp.org/article/view/466", abstract = "We correct two errors of omission in our paper, On L{\'e}vy processes conditioned to stay positive. \url{http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1517&layout=abstract} Electron. J. Probab. {\bf 10}, (2005), no. 28, 948--961. Math. Review 2006h:60079.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "L{\'e}vy process, conditioned to stay positive, weak convergence, excursion measure", } @Article{Kurkova:2008:LES, author = "Irina Kurkova", title = "Local Energy Statistics in Directed Polymers", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "2:5--2:25", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-475", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/475", abstract = "Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should, in most circumstances, be the same as in the random energy model. We show that this conjecture holds true as well for directed polymers in random environment. We also show that, under certain conditions, this conjecture holds for directed polymers even if energy levels that grow moderately with the volume of the system are considered.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Directed polymers", } @Article{Chen:2008:CPE, author = "Guan-Yu Chen and Laurent Saloff-Coste", title = "The Cutoff Phenomenon for Ergodic {Markov} Processes", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "3:26--3:78", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-474", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/474", abstract = "We consider the cutoff phenomenon in the context of families of ergodic Markov transition functions. This includes classical examples such as families of ergodic finite Markov chains and Brownian motion on families of compact Riemannian manifolds. We give criteria for the existence of a cutoff when convergence is measured in $ L^p$-norm, $ 1 < p < \infty $. This allows us to prove the existence of a cutoff in cases where the cutoff time is not explicitly known. In the reversible case, for $ 1 < p \leq \infty $, we show that a necessary and sufficient condition for the existence of a max-$ L^p$ cutoff is that the product of the spectral gap by the max-$ L^p$ mixing time tends to infinity. This type of condition was suggested by Yuval Peres. Illustrative examples are discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "cutoff phenomenon, ergodic Markov semigroups", } @Article{Miermont:2008:RPR, author = "Gr{\'e}gory Miermont and Mathilde Weill", title = "Radius and profile of random planar maps with faces of arbitrary degrees", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "4:79--4:106", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-478", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/478", abstract = "We prove some asymptotic results for the radius and the profile of large random planar maps with faces of arbitrary degrees. Using a bijection due to Bouttier, Di Francesco \& Guitter between rooted planar maps and certain four-type trees with positive labels, we derive our results from a conditional limit theorem for four-type spatial Galton--Watson trees.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian snake; invariance principle; multitype spatial Galton--Watson tree; Random planar map", } @Article{Houdre:2008:CSM, author = "Christian Houdr{\'e} and Hua Xu", title = "Concentration of the Spectral Measure for Large Random Matrices with Stable Entries", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "5:107--5:134", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-482", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/482", abstract = "We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries, in particular, stable or heavy tails ones. We also give concentration results for some other functionals of these random matrices, such as the largest eigenvalue or the largest singular value.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Spectral Measure, Random Matrices, Infinitely divisibility, Stable Vector, Concentration", } @Article{Fournier:2008:SLS, author = "Nicolas Fournier", title = "Smoothness of the law of some one-dimensional jumping S.D.E.s with non-constant rate of jump", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "6:135--6:156", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-480", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/480", abstract = "We consider a one-dimensional jumping Markov process, solving a Poisson-driven stochastic differential equation. We prove that the law of this process admits a smooth density for all positive times, under some regularity and non-degeneracy assumptions on the coefficients of the S.D.E. To our knowledge, our result is the first one including the important case of a non-constant rate of jump. The main difficulty is that in such a case, the process is not smooth as a function of its initial condition. This seems to make impossible the use of Malliavin calculus techniques. To overcome this problem, we introduce a new method, in which the propagation of the smoothness of the density is obtained by analytic arguments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic differential equations, Jump processes, Regularity of the density", } @Article{Savov:2008:CCR, author = "Mladen Savov", title = "Curve Crossing for the Reflected {L{\'e}vy} Process at Zero and Infinity", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "7:157--7:172", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-483", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/483", abstract = "Let $ R_t = \sup_{0 \leq s \leq t}X_s - X_t $ be a Levy process reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times above power law boundaries at infinity. Information as to when the expected passage time for $ R_t $ is finite, is given. We also discuss the almost sure finiteness of $ \limsup_{t \to 0}R_t / t^{\kappa } $, for each $ \kappa \geq 0 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Reflected process, passage times, power law boundaries", } @Article{Baurdoux:2008:MSG, author = "Erik Baurdoux and Andreas Kyprianou", title = "The {McKean} stochastic game driven by a spectrally negative {L{\'e}vy} process", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "8:173--8:197", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-484", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/484", abstract = "We consider the stochastic-game-analogue of McKean's optimal stopping problem when the underlying source of randomness is a spectrally negative L{\'e}vy process. Compared to the solution for linear Brownian motion given in Kyprianou (2004) one finds two new phenomena. Firstly the breakdown of smooth fit and secondly the stopping domain for one of the players `thickens' from a singleton to an interval, at least in the case that there is no Gaussian component.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic games, optimal stopping, pasting principles, fluctuation theory, L'evy processes", } @Article{Fill:2008:TPK, author = "James Fill and David Wilson", title = "Two-Player Knock 'em Down", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "9:198--9:212", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-485", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/485", abstract = "We analyze the two-player game of Knock 'em Down, asymptotically as the number of tokens to be knocked down becomes large. Optimal play requires mixed strategies with deviations of order $ \sqrt {n} $ from the na{\"\i}ve law-of-large numbers allocation. Upon rescaling by $ \sqrt {n} $ and sending $ n \to \infty $, we show that optimal play's random deviations always have bounded support and have marginal distributions that are absolutely continuous with respect to Lebesgue measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "game theory; Knock 'em Down; Nash equilibrium", } @Article{Caputo:2008:AEP, author = "Pietro Caputo and Fabio Martinelli and Fabio Toninelli", title = "On the Approach to Equilibrium for a Polymer with Adsorption and Repulsion", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "10:213--10:258", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-486", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/486", abstract = "We consider paths of a one-dimensional simple random walk conditioned to come back to the origin after $L$ steps, $ L \in 2 \mathbb {N}$. In the {\em pinning model} each path $ \eta $ has a weight $ \lambda^{N(\eta)}$, where $ \lambda > 0$ and $ N(\eta)$ is the number of zeros in $ \eta $. When the paths are constrained to be non-negative, the polymer is said to satisfy a hard-wall constraint. Such models are well known to undergo a localization/delocalization transition as the pinning strength $ \lambda $ is varied. In this paper we study a natural ``spin flip'' dynamics for associated to these models and derive several estimates on its spectral gap and mixing time. In particular, for the system with the wall we prove that relaxation to equilibrium is always at least as fast as in the free case (i.e., $ \lambda = 1$ without the wall), where the gap and the mixing time are known to scale as $ L^{-2}$ and $ L^2 \log L$, respectively. This improves considerably over previously known results. For the system without the wall we show that the equilibrium phase transition has a clear dynamical manifestation: for $ \lambda \geq 1$ relaxation is again at least as fast as the diffusive free case, but in the strictly delocalized phase ($ \lambda < 1$) the gap is shown to be $ O(L^{-5 / 2})$, up to logarithmic corrections. As an application of our bounds, we prove stretched exponential relaxation of local functions in the localized regime.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Coupling; Dynamical phase transition; Mixing time; Pinning model; Spectral gap", } @Article{Davydov:2008:SSD, author = "Youri Davydov and Ilya Molchanov and Sergei Zuyev", title = "Strictly stable distributions on convex cones", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "11:259--11:321", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-487", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/487", abstract = "Using the LePage representation, a symmetric alpha-stable random element in Banach space B with alpha from (0, 2) can be represented as a sum of points of a Poisson process in B. This point process is union-stable, i.e., the union of its two independent copies coincides in distribution with the rescaled original point process. This shows that the classical definition of stable random elements is closely related to the union-stability property of point processes. These concepts make sense in any convex cone, i.e., in a semigroup equipped with multiplication by numbers, and lead to a construction of stable laws in general cones by means of the LePage series. We prove that random samples (or binomial point processes) in rather general cones converge in distribution in the vague topology to the union-stable Poisson point process. This convergence holds also in a stronger topology, which implies that the sums of points converge in distribution to the sum of points of the union-stable point process. Since the latter corresponds to a stable law, this yields a limit theorem for normalised sums of random elements with alpha-stable limit for alpha from (0, 1). By using the technique of harmonic analysis on semigroups we characterise distributions of alpha-stable random elements and show how possible values of the characteristic exponent alpha relate to the properties of the semigroup and the corresponding scaling operation, in particular, their distributivity properties. It is shown that several conditions imply that a stable random element admits the LePage representation. The approach developed in the paper not only makes it possible to handle stable distributions in rather general cones (like spaces of sets or measures), but also provides an alternative way to prove classical limit theorems and deduce the LePage representation for strictly stable random vectors in Banach spaces.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "character; convex cone; Laplace transform; LePage series; L{\'e}vy measure; point process; Poisson process; random measure; random set; semigroup; stable distribution; union-stability", } @Article{Merlet:2008:CTS, author = "Glenn Merlet", title = "Cycle time of stochastic max-plus linear systems", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "12:322--12:340", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-488", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/488", abstract = "We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra. This type of recursive sequences are frequently used in applied probability as they model many systems as some queueing networks, train and computer networks, and production systems. We give a necessary condition for the recursive sequences to satisfy a strong law of large numbers, which proves to be sufficient when the matrices are i.i.d. Moreover, we construct a new example, in which the sequence of matrices is strongly mixing, that condition is satisfied, but the recursive sequence do not converges almost surely.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "law of large numbers; Markov chains; max-plus; products of random matrices; stochastic recursive sequences; subadditivity", } @Article{Lamberton:2008:PBA, author = "Damien Lamberton and Gilles Pag{\`e}s", title = "A penalized bandit algorithm", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "13:341--13:373", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-489", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/489", abstract = "We study a two armed-bandit recursive algorithm with penalty. We show that the algorithm converges towards its ``target'' although it always has a noiseless ``trap''. Then, we elucidate the rate of convergence. For some choices of the parameters, we obtain a central limit theorem in which the limit distribution is characterized as the unique stationary distribution of a Markov process with jumps.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "convergence rate; learning; penalization; stochastic approximation; Two-armed bandit algorithm", } @Article{Berestycki:2008:LBD, author = "Nathanael Berestycki and Rick Durrett", title = "Limiting behavior for the distance of a random walk", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "14:374--14:395", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-490", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/490", abstract = "In this paper we study some aspects of the behavior of random walks on large but finite graphs before they have reached their equilibrium distribution. This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from a linear regime to a sublinear regime at time $ n / 2 $. Here, we study the examples of random 3-regular graphs, random adjacent transpositions, and riffle shuffles. In the case of a random 3-regular graph, there is a phase transition where the speed changes from 1/3 to 0 at time $ 3 l o g_2 n $. A similar result is proved for riffle shuffles, where the speed changes from 1 to 0 at time $ l o g_2 n $. Both these changes occur when a distance equal to the average diameter of the graph is reached. However in the case of random adjacent transpositions, the behavior is more complex. We find that there is no phase transition, even though the distance has different scalings in three different regimes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walk, phase transition, adjacent transpositions, random regular graphs, riffle shuffles", } @Article{Lember:2008:IRR, author = "Jyri Lember and Heinrich Matzinger", title = "Information recovery from randomly mixed-up message text", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "15:396--15:466", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-491", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/491", abstract = "This paper is concerned with finding a fingerprint of a sequence. As input data one uses the sequence which has been randomly mixed up by observing it along a random walk path. A sequence containing order exp (n) bits receives a fingerprint with roughly n bits information. The fingerprint is characteristic for the original sequence. With high probability the fingerprint depends only on the initial sequence, but not on the random walk path.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walk in random environment; Scenery reconstruction", } @Article{Beghin:2008:PPG, author = "Luisa Beghin", title = "Pseudo-Processes Governed by Higher-Order Fractional Differential Equations", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "16:467--16:485", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-496", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/496", abstract = "We study here a heat-type differential equation of order $n$ greater than two, in the case where the time-derivative is supposed to be fractional. The corresponding solution can be described as the transition function of a pseudoprocess $ \Psi_n$ (coinciding with the one governed by the standard, non-fractional, equation) with a time argument $ \mathcal {T}_{\alpha }$ which is itself random. The distribution of $ \mathcal {T}_{\alpha }$ is presented together with some features of the solution (such as analytic expressions for its moments).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Fractional derivatives; Higher-order heat-type equations; Stable laws.; Wright functions", } @Article{Basdevant:2008:AAF, author = "Anne-Laure Basdevant and Christina Goldschmidt", title = "Asymptotics of the Allele Frequency Spectrum Associated with the {Bolthausen--Sznitman} Coalescent", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "17:486--17:512", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-494", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/494", abstract = "We consider a coalescent process as a model for the genealogy of a sample from a population. The population is subject to neutral mutation at constant rate $ \rho $ per individual and every mutation gives rise to a completely new type. The allelic partition is obtained by tracing back to the most recent mutation for each individual and grouping together individuals whose most recent mutations are the same. The allele frequency spectrum is the sequence $ (N_1 (n), N_2 (n), \ldots, N_n(n)) $, where $ N_k(n) $ is number of blocks of size $k$ in the allelic partition with sample size $n$. In this paper, we prove law of large numbers-type results for the allele frequency spectrum when the coalescent process is taken to be the Bolthausen--Sznitman coalescent. In particular, we show that $ n^{-1}(\log n) N_1 (n) {\stackrel {p}{\rightarrow }} \rho $ and, for $ k \geq 2$, $ n^{-1}(\log n)^2 N_k(n) {\stackrel {p}{\rightarrow }} \rho / (k(k - 1))$ as $ n \to \infty $. Our method of proof involves tracking the formation of the allelic partition using a certain Markov process, for which we prove a fluid limit.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Giacomin:2008:RCR, author = "Giambattista Giacomin", title = "Renewal convergence rates and correlation decay for homogeneous pinning models", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "18:513--18:529", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-497", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/497", abstract = "A class of discrete renewal processes with exponentially decaying inter-arrival distributions coincides with the infinite volume limit of general homogeneous pinning models in their localized phase. Pinning models are statistical mechanics systems to which a lot of attention has been devoted both for their relevance for applications and because they are solvable models exhibiting a non-trivial phase transition. The spatial decay of correlations in these systems is directly mapped to the speed of convergence to equilibrium for the associated renewal processes. We show that close to criticality, under general assumptions, the correlation decay rate, or the renewal convergence rate, coincides with the inter-arrival decay rate. We also show that, in general, this is false away from criticality. Under a stronger assumption on the inter-arrival distribution we establish a local limit theorem, capturing thus the sharp asymptotic behavior of correlations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Criticality; Decay of Correlations; Exponential Tails; Pinning Models; Renewal Theory; Speed of Convergence to Equilibrium", } @Article{Merkl:2008:BRE, author = "Franz Merkl and Silke Rolles", title = "Bounding a Random Environment Bounding a Random Environment for Two-dimensional Edge-reinforced Random Walk", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "19:530--19:565", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-495", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/495", abstract = "We consider edge-reinforced random walk on the infinite two-dimensional lattice. The process has the same distribution as a random walk in a certain strongly dependent random environment, which can be described by random weights on the edges. In this paper, we show some decay properties of these random weights. Using these estimates, we derive bounds for some hitting probabilities of the edge-reinforced random walk.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random environment; Reinforced random walk", } @Article{Daly:2008:UBS, author = "Fraser Daly", title = "Upper Bounds for {Stein}-Type Operators", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "20:566--20:587", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-479", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/479", abstract = "We present sharp bounds on the supremum norm of $ \mathcal {D}^j S h $ for $ j \geq 2 $, where $ \mathcal {D} $ is the differential operator and $S$ the Stein operator for the standard normal distribution. The same method is used to give analogous bounds for the exponential, Poisson and geometric distributions, with $ \mathcal {D}$ replaced by the forward difference operator in the discrete case. We also discuss applications of these bounds to the central limit theorem, simple random sampling, Poisson--Charlier approximation and geometric approximation using stochastic orderings.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem; Poisson--Charlier approximation; Stein's method; Stein-type operator; stochastic ordering", } @Article{Bose:2008:ALM, author = "Arup Bose and Arnab Sen", title = "Another look at the moment method for large dimensional random matrices", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "21:588--21:628", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-501", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/501", abstract = "The methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices includes the well known moment method which invokes the trace formula. Its success has been demonstrated in several types of matrices such as the Wigner matrix and the sample variance covariance matrix. In a recent article Bryc, Dembo and Jiang (2006) establish the LSD for the random Toeplitz and Hankel matrices using the moment method. They perform the necessary counting of terms in the trace by splitting the relevant sets into equivalent classes and relating the limits of the counts to certain volume calculations.\par We build on their work and present a unified approach. This helps provide relatively short and easy proofs for the LSD of common matrices while at the same time providing insight into the nature of different LSD and their interrelations. By extending these methods we are also able to deal with matrices with appropriate dependent entries.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bounded Lipschitz metric, large dimensional random matrices, eigenvalues, Wigner matrix, sample variance covariance matrix, Toeplitz matrix, Hankel matrix, circulant matrix, symmetric circulant matrix, reverse circulant matrix, palindromic matrix, limit", } @Article{Conus:2008:NLS, author = "Daniel Conus and Robert Dalang", title = "The Non-Linear Stochastic Wave Equation in High Dimensions", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "22:629--22:670", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-500", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/500", abstract = "We propose an extension of Walsh's classical martingale measure stochastic integral that makes it possible to integrate a general class of Schwartz distributions, which contains the fundamental solution of the wave equation, even in dimensions greater than 3. This leads to a square-integrable random-field solution to the non-linear stochastic wave equation in any dimension, in the case of a driving noise that is white in time and correlated in space. In the particular case of an affine multiplicative noise, we obtain estimates on $p$-th moments of the solution ($ p \geq 1$), and we show that the solution is H{\"o}lder continuous. The H{\"o}lder exponent that we obtain is optimal.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "H{\"o}lder continuity; Martingale measures; moment formulae; stochastic integration; stochastic partial differential equations; stochastic wave equation", } @Article{Holmes:2008:CLT, author = "Mark Holmes", title = "Convergence of Lattice Trees to Super-{Brownian} Motion above the Critical Dimension", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "23:671--23:755", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-499", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/499", abstract = "We use the lace expansion to prove asymptotic formulae for the Fourier transforms of the $r$-point functions for a spread-out model of critically weighted lattice trees on the $d$-dimensional integer lattice for $ d > 8$. A lattice tree containing the origin defines a sequence of measures on the lattice, and the statistical mechanics literature gives rise to a natural probability measure on the collection of such lattice trees. Under this probability measure, our results, together with the appropriate limiting behaviour for the survival probability, imply convergence to super-Brownian excursion in the sense of finite-dimensional distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "lace expansion.; Lattice trees; super-Brownian motion", } @Article{Roellin:2008:SCB, author = "Adrian Roellin", title = "Symmetric and centered binomial approximation of sums of locally dependent random variables", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "24:756--24:776", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-503", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/503", abstract = "Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric binomial distribution, serving as a natural alternative to the normal distribution in discrete settings. The bounds are given with respect to the total variation and a local limit metric. Under appropriate smoothness properties of the summands, the same order of accuracy as in the Berry--Ess{\'e}en Theorem is achieved. The approximation of the total number of points of a point processes is also considered. The results are applied to the exceedances of the $r$-scans process and to the Mat{\'e}rn hardcore point process type I to obtain explicit bounds with respect to the two metrics.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "binomial distribution; local dependence; Stein's method; total variation metric", } @Article{Champagnat:2008:LTC, author = "Nicolas Champagnat and Sylvie Roelly", title = "Limit theorems for conditioned multitype {Dawson--Watanabe} processes and {Feller} diffusions", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "25:777--25:810", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-504", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/504", abstract = "A multitype Dawson--Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process-the conditioned multitype Feller branching diffusion-are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "conditioned Dawson--Watanabe process; conditioned Feller diffusion; critical and subcritical Dawson--Watanabe process; long time behavior.; multitype measure-valued branching processes; remote survival", } @Article{Basdevant:2008:RGT, author = "Anne-Laure Basdevant and Arvind Singh", title = "Rate of growth of a transient cookie random walk", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "26:811--26:851", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-498", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/498", abstract = "We consider a one-dimensional transient cookie random walk. It is known from a previous paper (BS2008) that a cookie random walk $ (X_n) $ has positive or zero speed according to some positive parameter $ \alpha > 1 $ or $ \leq 1 $. In this article, we give the exact rate of growth of $ X_n $ in the zero speed regime, namely: for $ 0 < \alpha < 1 $, $ X_n / n^{(? + 1) / 2} $ converges in law to a Mittag-Leffler distribution whereas for $ \alpha = 1 $, $ X_n(\log n) / n $ converges in probability to some positive constant.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching process with migration; cookie or multi-excited random walk; Rates of transience", } @Article{Petrou:2008:MCL, author = "Evangelia Petrou", title = "{Malliavin} Calculus in {L{\'e}vy} spaces and Applications to Finance", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "27:852--27:879", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-502", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/502", abstract = "The main goal of this paper is to generalize the results of Fournie et al. [7] for markets generated by L{\'e}vy processes. For this reason we extend the theory of Malliavin calculus to provide the tools that are necessary for the calculation of the sensitivities, such as differentiability results for the solution of a stochastic differential equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Windisch:2008:LCV, author = "David Windisch", title = "Logarithmic Components of the Vacant Set for Random Walk on a Discrete Torus", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "28:880--28:897", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-506", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/506", abstract = "This work continues the investigation, initiated in a recent work by Benjamini and Sznitman, of percolative properties of the set of points not visited by a random walk on the discrete torus $ ({\mathbb Z} / N{\mathbb Z})^d $ up to time $ u N^d $ in high dimension $d$. If $ u > 0$ is chosen sufficiently small it has been shown that with overwhelming probability this vacant set contains a unique giant component containing segments of length $ c_0 \log N$ for some constant $ c_0 > 0$, and this component occupies a non-degenerate fraction of the total volume as $N$ tends to infinity. Within the same setup, we investigate here the complement of the giant component in the vacant set and show that some components consist of segments of logarithmic size. In particular, this shows that the choice of a sufficiently large constant $ c_0 > 0$ is crucial in the definition of the giant component.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "discrete torus; Giant component; random walk; vacant set", } @Article{Boufoussi:2008:PPC, author = "Brahim Boufoussi and Marco Dozzi and Raby Guerbaz", title = "Path properties of a class of locally asymptotically self similar processes", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "29:898--29:921", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-505", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/505", abstract = "Various paths properties of a stochastic process are obtained under mild conditions which allow for the integrability of the characteristic function of its increments and for the dependence among them. The main assumption is closely related to the notion of local asymptotic self-similarity. New results are obtained for the class of multifractional random processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Hausdorff dimension, level sets, local asymptotic self-similarity, local non-determinism, local times", } @Article{Reynolds:2008:DRS, author = "David Reynolds and John Appleby", title = "Decay Rates of Solutions of Linear Stochastic {Volterra} Equations", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "30:922--30:943", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-507", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/507", abstract = "The paper studies the exponential and non--exponential convergence rate to zero of solutions of scalar linear convolution It{\^o}-Volterra equations in which the noise intensity depends linearly on the current state. By exploiting the positivity of the solution, various upper and lower bounds in first mean and almost sure sense are obtained, including Liapunov exponents.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "almost sure exponential asymptotic stability, Liapunov exponent, subexponential distribution, subexponential function, Volterra equations, It{\^o}-Volterra equations", } @Article{Menshikov:2008:URR, author = "Mikhail Menshikov and Stanislav Volkov", title = "Urn-related random walk with drift $ \rho x^\alpha / t^\beta $", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "31:944--31:960", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-508", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/508", abstract = "We study a one-dimensional random walk whose expected drift depends both on time and the position of a particle. We establish a non-trivial phase transition for the recurrence vs. transience of the walk, and show some interesting applications to Friedman's urn, as well as showing the connection with Lamperti's walk with asymptotically zero drift.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "martingales; Random walks; urn models", } @Article{Kulik:2008:SEV, author = "Rafal Kulik", title = "Sums of extreme values of subordinated long-range dependent sequences: moving averages with finite variance", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "32:961--32:979", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-510", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/510", abstract = "In this paper we study the limiting behavior of sums of extreme values of long range dependent sequences defined as functionals of linear processes with finite variance. If the number of extremes in a sum is large enough, we obtain asymptotic normality, however, the scaling factor is relatively bigger than in the i.i.d case, meaning that the maximal terms have relatively smaller contribution to the whole sum. Also, it is possible for a particular choice of a model, that the scaling need not to depend on the tail index of the underlying marginal distribution, as it is well-known to be so in the i.i.d. situation. Furthermore, subordination may change the asymptotic properties of sums of extremes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "sample quantiles, linear processes, empirical processes, long range dependence, sums of extremes, trimmed sums", } @Article{Broman:2008:LLC, author = "Erik Broman and Federico Camia", title = "Large-{$N$} Limit of Crossing Probabilities, Discontinuity, and Asymptotic Behavior of Threshold Values in {Mandelbrot}'s Fractal Percolation Process", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "33:980--33:999", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-511", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/511", abstract = "We study Mandelbrot's percolation process in dimension $ d \geq 2 $. The process generates random fractal sets by an iterative procedure which starts by dividing the unit cube $ [0, 1]^d $ in $ N^d $ subcubes, and independently retaining or discarding each subcube with probability $p$ or $ 1 - p$ respectively. This step is then repeated within the retained subcubes at all scales. As $p$ is varied, there is a percolation phase transition in terms of paths for all $ d \geq 2$, and in terms of $ (d - 1)$-dimensional ``sheets'' for all $ d \geq 3$.\par For any $ d \geq 2$, we consider the random fractal set produced at the path-percolation critical value $ p_c(N, d)$, and show that the probability that it contains a path connecting two opposite faces of the cube $ [0, 1]^d$ tends to one as $ N \to \infty $. As an immediate consequence, we obtain that the above probability has a discontinuity, as a function of $p$, at $ p_c(N, d)$ for all $N$ sufficiently large. This had previously been proved only for $ d = 2$ (for any $ N \geq 2$). For $ d \geq 3$, we prove analogous results for sheet-percolation.\par In dimension two, Chayes and Chayes proved that $ p_c(N, 2)$ converges, as $ N \to \infty $, to the critical density $ p_c$ of site percolation on the square lattice. Assuming the existence of the correlation length exponent $ \nu $ for site percolation on the square lattice, we establish the speed of convergence up to a logarithmic factor. In particular, our results imply that $ p_c(N, 2) - p_c = (\frac {1}{N})^{1 / \nu + o(1)}$ as $ N \to \infty $, showing an interesting relation with near-critical percolation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "critical probability; crossing probability; enhancement/diminishment percolation; Fractal percolation; near-critical percolation", } @Article{Adamczak:2008:TIS, author = "Radoslaw Adamczak", title = "A tail inequality for suprema of unbounded empirical processes with applications to {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "34:1000--34:1034", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-521", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/521", abstract = "We present a tail inequality for suprema of empirical processes generated by variables with finite $ \psi_\alpha $ norms and apply it to some geometrically ergodic Markov chains to derive similar estimates for empirical processes of such chains, generated by bounded functions. We also obtain a bounded difference inequality for symmetric statistics of such Markov chains.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "concentration inequalities, empirical processes, Markov chains", } @Article{Matoussi:2008:SSS, author = "Anis Matoussi and Mingyu Xu", title = "{Sobolev} solution for semilinear {PDE} with obstacle under monotonicity condition", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "35:1035--35:1067", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-522", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/522", abstract = "We prove the existence and uniqueness of Sobolev solution of a semilinear PDE's and PDE's with obstacle under monotonicity condition. Moreover we give the probabilistic interpretation of the solutions in term of Backward SDE and reflected Backward SDE respectively", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Backward stochastic differential equation, Reflected backward stochastic differential equation, monotonicity condition, Stochastic flow, partial differential equation with obstacle", } @Article{DeBlassie:2008:EPB, author = "Dante DeBlassie", title = "The Exit Place of {Brownian} Motion in the Complement of a Horn", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "36:1068--36:1095", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-524", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/524", abstract = "Consider the domain lying outside a horn. We determine asymptotics of the logarithm of the chance that Brownian motion in the domain has a large exit place. For a certain class of horns, the behavior is given explicitly in terms of the geometry of the domain. We show that for some horns the behavior depends on the dimension, whereas for other horns, it does not. Analytically, the result is equivalent to estimating the harmonic measure of the part of the domain lying outside a cylinder with large diameter.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Horn-shaped domain, $h$-transform, Feynman--Kac representation, exit place of Brownian motion, harmonic measure", } @Article{Zambotti:2008:CEB, author = "Lorenzo Zambotti", title = "A conservative evolution of the {Brownian} excursion", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "37:1096--37:1119", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-525", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/525", abstract = "We consider the problem of conditioning the Brownian excursion to have a fixed time average over the interval [0, 1] and we study an associated stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space-time white noise and contains a double Laplacian in the drift. Due to the lack of the maximum principle for the double Laplacian, the standard techniques based on the penalization method do not yield existence of a solution.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian excursion; Brownian meander; singular conditioning; Stochastic partial differential equations with reflection", } @Article{Baudoin:2008:SSF, author = "Fabrice Baudoin and Laure Coutin", title = "Self-similarity and fractional {Brownian} motion on {Lie} groups", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "38:1120--38:1139", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-530", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/530", abstract = "The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this process has stationary increments and satisfies a local self-similar property. Furthermore the Lie groups for which this self-similar property is global are characterized.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Fractional Brownian motion, Lie group", } @Article{Basse:2008:GMA, author = "Andreas Basse", title = "{Gaussian} Moving Averages and Semimartingales", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "39:1140--39:1165", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-526", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/526", abstract = "In the present paper we study moving averages (also known as stochastic convolutions) driven by a Wiener process and with a deterministic kernel. Necessary and sufficient conditions on the kernel are provided for the moving average to be a semimartingale in its natural filtration. Our results are constructive - meaning that they provide a simple method to obtain kernels for which the moving average is a semimartingale or a Wiener process. Several examples are considered. In the last part of the paper we study general Gaussian processes with stationary increments. We provide necessary and sufficient conditions on spectral measure for the process to be a semimartingale.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian processes; moving averages; non-canonical representations; semimartingales; stationary processes; stochastic convolutions", } @Article{Alberts:2008:HDS, author = "Tom Alberts and Scott Sheffield", title = "{Hausdorff} Dimension of the {SLE} Curve Intersected with the Real Line", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "40:1166--40:1188", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-515", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/515", abstract = "We establish an upper bound on the asymptotic probability of an $ S L E(\kappa) $ curve hitting two small intervals on the real line as the interval width goes to zero, for the range $ 4 < \kappa < 8 $. As a consequence we are able to prove that the random set of points in $R$ hit by the curve has Hausdorff dimension $ 2 - 8 / \kappa $, almost surely.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Hausdorff dimension; SLE; Two-point hitting probability", } @Article{Muller:2008:CTM, author = "Sebastian M{\"u}ller", title = "A criterion for transience of multidimensional branching random walk in random environment", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "41:1189--41:1202", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-517", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/517", abstract = "We develop a criterion for transience for a general model of branching Markov chains. In the case of multi-dimensional branching random walk in random environment (BRWRE) this criterion becomes explicit. In particular, we show that Condition L of Comets and Popov [3] is necessary and sufficient for transience as conjectured. Furthermore, the criterion applies to two important classes of branching random walks and implies that the critical branching random walk is transient resp. dies out locally.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching Markov chains; random environment, spectral radius; recurrence; transience", } @Article{Cox:2008:CMW, author = "Alexander Cox and Jan Obloj", title = "Classes of measures which can be embedded in the Simple Symmetric Random Walk", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "42:1203--42:1228", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-516", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/516", abstract = "We characterize the possible distributions of a stopped simple symmetric random walk $ X_\tau $, where $ \tau $ is a stopping time relative to the natural filtration of $ (X_n) $. We prove that any probability measure on $ \mathbb {Z} $ can be achieved as the law of $ X_\tau $ where $ \tau $ is a minimal stopping time, but the set of measures obtained under the further assumption that $ (X_{n \land \tau } \colon n \geq 0) $ is a uniformly integrable martingale is a fractal subset of the set of all centered probability measures on $ \mathbb {Z} $. This is in sharp contrast to the well-studied Brownian motion setting. We also investigate the discrete counterparts of the Chacon-Walsh (1976) and Azema-Yor (1979) embeddings and show that they lead to yet smaller sets of achievable measures. Finally, we solve explicitly the Skorokhod embedding problem constructing, for a given measure $ \mu $, a minimal stopping time $ \tau $ which embeds $ \mu $ and which further is uniformly integrable whenever a uniformly integrable embedding of $ \mu $ exists.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Azema-Yor stopping time; Chacon-Walsh stopping time; fractal; iterated function system; minimal stopping time; random walk; self-similar set; Skorokhod embedding problem; uniform integrability", } @Article{Nourdin:2008:WPV, author = "Ivan Nourdin and Giovanni Peccati", title = "Weighted power variations of iterated {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "43:1229--43:1256", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-534", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/534", abstract = "We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional distributions, and show that the laws of the limiting objects can always be expressed in terms of three independent Brownian motions $ X, Y $ and $B$, as well as of the local times of $Y$. In particular, our results involve ''weighted'' versions of Kesten and Spitzer's Brownian motion in random scenery. Our findings extend the theory initiated by Khoshnevisan and Lewis (1999), and should be compared with the recent result by Nourdin and R{\'e}veillac (2008), concerning the weighted power variations of fractional Brownian motion with Hurst index $ H = 1 / 4$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; Brownian motion in random scenery; Iterated Brownian motion; Limit theorems; Weighted power variations", } @Article{Gibson:2008:MSV, author = "Lee Gibson", title = "The mass of sites visited by a random walk on an infinite graph", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "44:1257--44:1282", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-531", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/531", abstract = "We determine the log-asymptotic decay rate of the negative exponential moments of the mass of sites visited by a random walk on an infinite graph which satisfies a two-sided sub-Gaussian estimate on its transition kernel. This provides a new method of proof of the correct decay rate for Cayley graphs of finitely generated groups with polynomial volume growth. This method also extend known results by determining this decay rate for certain graphs with fractal-like structure or with non-Alfors regular volume growth functions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walk, infinite graph, visited sites, asymptotic decay rates, polynomial volume growth, Cayley graph, fractal graph, Alfors regular", } @Article{Davies:2008:SAN, author = "Ian Davies", title = "Semiclassical Analysis and a New Result for {Poisson--L{\'e}vy} Excursion Measures", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "45:1283--45:1306", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-513", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/513", abstract = "The Poisson--L{\'e}vy excursion measure for the diffusion process with small noise satisfying the It{\^o} equation\par $$ d X^{\varepsilon } = b(X^{\varepsilon }(t))d t + \sqrt \varepsilon \, d B(t) $$ is studied and the asymptotic behaviour in $ \varepsilon $ is investigated. The leading order term is obtained exactly and it is shown that at an equilibrium point there are only two possible forms for this term --- Levy or Hawkes--Truman. We also compute the next to leading order.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "excursion measures, asymptotic expansions", } @Article{Eichelsbacher:2008:ORW, author = "Peter Eichelsbacher and Wolfgang K{\"o}nig", title = "Ordered Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "46:1307--46:1336", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-539", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/539", abstract = "We construct the conditional version of $k$ independent and identically distributed random walks on $R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random walks, the discrete variant of Dyson's Brownian motions, which have been considered yet only for nearest-neighbor walks on the lattice. Our only assumptions are moment conditions on the steps and the validity of the local central limit theorem. The conditional process is constructed as a Doob $h$-transform with some positive regular function $V$ that is strongly related with the Vandermonde determinant and reduces to that function for simple random walk. Furthermore, we prove an invariance principle, i.e., a functional limit theorem towards Dyson's Brownian motions, the continuous analogue.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Doob h-transform; Dyson's Brownian motions; fluctuation theory.; non-colliding random walks; non-intersecting random processes; Vandermonde determinant", } @Article{Kulske:2008:PMG, author = "Christof K{\"u}lske and Alex Opoku", title = "The posterior metric and the goodness of {Gibbsianness} for transforms of {Gibbs} measures", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "47:1307--47:1344", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-560", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/560", abstract = "We present a general method to derive continuity estimates for conditional probabilities of general (possibly continuous) spin models subjected to local transformations. Such systems arise in the study of a stochastic time-evolution of Gibbs measures or as noisy observations. Assuming no a priori metric on the local state spaces but only a measurable structure, we define the posterior metric on the local image space. We show that it allows in a natural way to divide the local part of the continuity estimates from the spatial part (which is treated by Dobrushin uniqueness here). We show in the concrete example of the time evolution of rotators on the $ (q - 1)$-dimensional sphere how this method can be used to obtain estimates in terms of the familiar Euclidean metric. In another application we prove the preservation of Gibbsianness for sufficiently fine local coarse-grainings when the Hamiltonian satisfies a Lipschitz property", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "phase transitions; posterior metric; specification; Time-evolved Gibbs measures, non-Gibbsian measures: Dobrushin uniqueness", } @Article{Collet:2008:RPS, author = "Pierre Collet and Antonio Galves and Florencia Leonardi", title = "Random perturbations of stochastic processes with unbounded variable length memory", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "48:1345--48:1361", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-538", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/538", abstract = "We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "chains of infinite order, variable length Markov chains, chains with unbounded variable length memory, random perturbations, algorithm Context, context trees", } @Article{Bonaccorsi:2008:SFN, author = "Stefano Bonaccorsi and Carlo Marinelli and Giacomo Ziglio", title = "Stochastic {FitzHugh--Nagumo} equations on networks with impulsive noise", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "49:1362--49:1379", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-532", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/532", abstract = "We consider a system of nonlinear partial differential equations with stochastic dynamical boundary conditions that arises in models of neurophysiology for the diffusion of electrical potentials through a finite network of neurons. Motivated by the discussion in the biological literature, we impose a general diffusion equation on each edge through a generalized version of the FitzHugh--Nagumo model, while the noise acting on the boundary is described by a generalized stochastic Kirchhoff law on the nodes. In the abstract framework of matrix operators theory, we rewrite this stochastic boundary value problem as a stochastic evolution equation in infinite dimensions with a power-type nonlinearity, driven by an additive L{\'e}vy noise. We prove global well-posedness in the mild sense for such stochastic partial differential equation by monotonicity methods.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic PDEs, FitzHugh--Nagumo equation, L{\'e}vy processes, maximal monotone operators", } @Article{Borodin:2008:LTA, author = "Alexei Borodin and Patrik Ferrari", title = "Large time asymptotics of growth models on space-like paths {I}: {PushASEP}", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "50:1380--50:1418", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-541", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/541", abstract = "We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of the height function of the associated growth model along any space-like path are described by the Airy$_1$ and Airy$_2$ processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic growth, KPZ, determinantal processes, Airy processes", } @Article{Croydon:2008:RWG, author = "David Croydon and Takashi Kumagai", title = "Random walks on {Galton--Watson} trees with infinite variance offspring distribution conditioned to survive", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "51:1419--51:1441", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-536", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/536", abstract = "We establish a variety of properties of the discrete time simple random walk on a Galton--Watson tree conditioned to survive when the offspring distribution, $Z$ say, is in the domain of attraction of a stable law with index $ \alpha \in (1, 2]$. In particular, we are able to prove a quenched version of the result that the spectral dimension of the random walk is $ 2 \alpha / (2 \alpha - 1)$. Furthermore, we demonstrate that when $ \alpha \in (1, 2)$ there are logarithmic fluctuations in the quenched transition density of the simple random walk, which contrasts with the log-logarithmic fluctuations seen when $ \alpha = 2$. In the course of our arguments, we obtain tail bounds for the distribution of the $n$ th generation size of a Galton--Watson branching process with offspring distribution $Z$ conditioned to survive, as well as tail bounds for the distribution of the total number of individuals born up to the $n$ th generation, that are uniform in $n$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching process; random walk; stable distribution; transition density", } @Article{Schweinsberg:2008:WM, author = "Jason Schweinsberg", title = "Waiting for $m$ mutations", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "52:1442--52:1478", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-540", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/540", abstract = "We consider a model of a population of fixed size $N$ in which each individual gets replaced at rate one and each individual experiences a mutation at rate $ \mu $. We calculate the asymptotic distribution of the time that it takes before there is an individual in the population with $m$ mutations. Several different behaviors are possible, depending on how ?? changes with $N$. These results have applications to the problem of determining the waiting time for regulatory sequences to appear and to models of cancer development.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Moran model; mutations; population genetics; Waiting times", } @Article{Voss:2008:LDO, author = "Jochen Voss", title = "Large Deviations for One Dimensional Diffusions with a Strong Drift", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "53:1479--53:1528", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-564", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/564", abstract = "We derive a large deviation principle which describes the behaviour of a diffusion process with additive noise under the influence of a strong drift. Our main result is a large deviation theorem for the distribution of the end-point of a one-dimensional diffusion with drift $ \theta b $ where $b$ is a drift function and $ \theta $ a real number, when $ \theta $ converges to $ \infty $. It transpires that the problem is governed by a rate function which consists of two parts: one contribution comes from the Freidlin--Wentzell theorem whereas a second term reflects the cost for a Brownian motion to stay near a equilibrium point of the drift over long periods of time.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "diffusion processes; large deviations; stochastic differential equations", } @Article{Confortola:2008:QBR, author = "Fulvia Confortola and Philippe Briand", title = "Quadratic {BSDEs} with Random Terminal Time and Elliptic {PDEs} in Infinite Dimension", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "54:1529--54:1561", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-514", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/514", abstract = "In this paper we study one dimensional backward stochastic differential equations (BSDEs) with random terminal time not necessarily bounded or finite when the generator $ F(t, Y, Z) $ has a quadratic growth in $Z$. We provide existence and uniqueness of a bounded solution of such BSDEs and, in the case of infinite horizon, regular dependence on parameters. The obtained results are then applied to prove existence and uniqueness of a mild solution to elliptic partial differential equations in Hilbert spaces. Finally we show an application to a control problem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "elliptic PDEs; optimal stochastic control; Quadratic BSDEs", } @Article{Nolin:2008:NCP, author = "Pierre Nolin", title = "Near-critical percolation in two dimensions", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "55:1562--55:1623", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-565", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/565", abstract = "We give a self-contained and detailed presentation of Kesten's results that allow to relate critical and near-critical percolation on the triangular lattice. They constitute an important step in the derivation of the exponents describing the near-critical behavior of this model. For future use and reference, we also show how these results can be obtained in more general situations, and we state some new consequences.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "arm events; critical exponents; near-critical percolation", } @Article{Albenque:2008:SFI, author = "Marie Albenque and Jean-Fran{\c{c}}ois Marckert", title = "Some families of increasing planar maps", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "56:1624--56:1671", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-563", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/563", abstract = "Stack-triangulations appear as natural objects when one wants to define some families of increasing triangulations by successive additions of faces. We investigate the asymptotic behavior of rooted stack-triangulations with $ 2 n $ faces under two different distributions. We show that the uniform distribution on this set of maps converges, for a topology of local convergence, to a distribution on the set of infinite maps. In the other hand, we show that rescaled by $ n^{1 / 2} $, they converge for the Gromov--Hausdorff topology on metric spaces to the continuum random tree introduced by Aldous. Under a distribution induced by a natural random construction, the distance between random points rescaled by $ (6 / 11) \log n $ converge to 1 in probability. We obtain similar asymptotic results for a family of increasing quadrangulations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stackmaps, triangulations, Gromov--Hausdorff convergence, continuum random tree", } @Article{Kyprianou:2008:SCC, author = "Andreas Kyprianou and Victor Rivero", title = "Special, conjugate and complete scale functions for spectrally negative {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "57:1672--57:1701", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-567", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/567", abstract = "Following from recent developments in Hubalek and Kyprianou [28], the objective of this paper is to provide further methods for constructing new families of scale functions for spectrally negative L{\'e}vy processes which are completely explicit. This is the result of an observation in the aforementioned paper which permits feeding the theory of Bernstein functions directly into the Wiener--Hopf factorization for spectrally negative L{\'e}vy processes. Many new, concrete examples of scale functions are offered although the methodology in principle delivers still more explicit examples than those listed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Potential theory for subordinators, Scale functions, Special subordinators, Spectrally negative L{\'e}vy processes", } @Article{Lyons:2008:EUS, author = "Russell Lyons and Benjamin Morris and Oded Schramm", title = "Ends in Uniform Spanning Forests", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "58:1702--58:1725", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-566", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/566", abstract = "It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cayley graphs.; Spanning trees", } @Article{Gayrard:2008:EPT, author = "V{\'e}ronique Gayrard and G{\'e}rard Ben Arous", title = "Elementary potential theory on the hypercube", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "59:1726--59:1807", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-527", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/527", abstract = "This work addresses potential theoretic questions for the standard nearest neighbor random walk on the hypercube $ \{ - 1, + 1 \}^N $. For a large class of subsets $ A \subset \{ - 1, + 1 \}^N $ we give precise estimates for the harmonic measure of $A$, the mean hitting time of $A$, and the Laplace transform of this hitting time. In particular, we give precise sufficient conditions for the harmonic measure to be asymptotically uniform, and for the hitting time to be asymptotically exponentially distributed, as $ N \rightarrow \infty $. Our approach relies on a $d$-dimensional extension of the Ehrenfest urn scheme called lumping and covers the case where $d$ is allowed to diverge with $N$ as long as $ d \leq \alpha_0 \frac {N}{\log N}$ for some constant $ 0 < \alpha_0 < 1$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walk on hypercubes, lumping", } @Article{Bass:2008:DSD, author = "Richard Bass and Edwin Perkins", title = "Degenerate stochastic differential equations arising from catalytic branching networks", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "60:1808--60:1885", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-568", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/568", abstract = "We establish existence and uniqueness for the martingale problem associated with a system of degenerate SDE's representing a catalytic branching network. The drift and branching coefficients are only assumed to be continuous and satisfy some natural non-degeneracy conditions. We assume at most one catalyst per site as is the case for the hypercyclic equation. Here the two-dimensional case with affine drift is required in work of [DGHSS] on mean fields limits of block averages for 2-type branching models on a hierarchical group. The proofs make use of some new methods, including Cotlar's lemma to establish asymptotic orthogonality of the derivatives of an associated semigroup at different times, and a refined integration by parts technique from [DP1].", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "catalytic branching; Cotlar's lemma; degenerate diffusions; martingale problem; perturbations; resolvents; stochastic differential equations", } @Article{Piera:2008:CRR, author = "Francisco Piera and Ravi Mazumdar", title = "Comparison Results for Reflected Jump-diffusions in the Orthant with Variable Reflection Directions and Stability Applications", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "61:1886--61:1908", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-569", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/569", abstract = "We consider reflected jump-diffusions in the orthant $ R_+^n $ with time- and state-dependent drift, diffusion and jump-amplitude coefficients. Directions of reflection upon hitting boundary faces are also allow to depend on time and state. Pathwise comparison results for this class of processes are provided, as well as absolute continuity properties for their associated regulator processes responsible of keeping the respective diffusions in the orthant. An important role is played by the boundary property in that regulators do not charge times spent by the reflected diffusion at the intersection of two or more boundary faces. The comparison results are then applied to provide an ergodicity condition for the state-dependent reflection directions case.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "ergodicity.; Jump-diffusion processes; pathwise comparisons; Skorokhod maps; stability; state-dependent oblique reflections", } @Article{Veto:2008:SRR, author = "Balint Veto and Balint Toth", title = "Self-repelling random walk with directed edges on {$ \mathbb {Z} $}", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "62:1909--62:1926", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-570", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/570", abstract = "We consider a variant of self-repelling random walk on the integer lattice Z where the self-repellence is defined in terms of the local time on oriented edges. The long-time asymptotic scaling of this walk is surprisingly different from the asymptotics of the similar process with self-repellence defined in terms of local time on unoriented edges. We prove limit theorems for the local time process and for the position of the random walker. The main ingredient is a Ray--Knight-type of approach. At the end of the paper, we also present some computer simulations which show the strange scaling behaviour of the walk considered.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walks with long memory, self-repelling, one dimension, oriented edges, local time, Ray--Knight-theory, coupling", } @Article{Amir:2008:SSE, author = "Gideon Amir and Christopher Hoffman", title = "A special set of exceptional times for dynamical random walk on {$ Z^2 $}", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "63:1927--63:1951", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-571", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/571", abstract = "In [2] Benjamini, H{\"a}ggstr{\"o}m, Peres and Steif introduced the model of dynamical random walk on the $d$-dimensional lattice $ Z^d$. This is a continuum of random walks indexed by a time parameter $t$. They proved that for dimensions $ d = 3, 4$ there almost surely exist times $t$ such that the random walk at time $t$ visits the origin infinitely often, but for dimension 5 and up there almost surely do not exist such $t$. Hoffman showed that for dimension 2 there almost surely exists $t$ such that the random walk at time $t$ visits the origin only finitely many times [5]. We refine the results of [5] for dynamical random walk on $ Z^2$, showing that with probability one the are times when the origin is visited only a finite number of times while other points are visited infinitely often.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dynamical Random Walks, Dynamical Sensativity; Random Walks", } @Article{Kosygina:2008:PNE, author = "Elena Kosygina and Martin Zerner", title = "Positively and negatively excited random walks on integers, with branching processes", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "64:1952--64:1979", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-572", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/572", abstract = "We consider excited random walks on the integers with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right. We extend the criteria for recurrence and transience by M. Zerner and for positivity of speed by A.-L. Basdevant and A. Singh to this case and also prove an annealed central limit theorem. The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central limit theorem; excited random walk; law of large numbers; positive and negative cookies; recurrence; renewal structure; transience", } @Article{Bianchi:2008:GDN, author = "Alessandra Bianchi", title = "{Glauber} dynamics on nonamenable graphs: boundary conditions and mixing time", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "65:1980--65:2012", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-574", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/574", abstract = "We study the stochastic Ising model on finite graphs with n vertices and bounded degree and analyze the effect of boundary conditions on the mixing time. We show that for all low enough temperatures, the spectral gap of the dynamics with (+)-boundary condition on a class of nonamenable graphs, is strictly positive uniformly in n. This implies that the mixing time grows at most linearly in n. The class of graphs we consider includes hyperbolic graphs with sufficiently high degree, where the best upper bound on the mixing time of the free boundary dynamics is polynomial in n, with exponent growing with the inverse temperature. In addition, we construct a graph in this class, for which the mixing time in the free boundary case is exponentially large in n. This provides a first example where the mixing time jumps from exponential to linear in n while passing from free to (+)-boundary condition. These results extend the analysis of Martinelli, Sinclair and Weitz to a wider class of nonamenable graphs.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Glauber dynamics; mixing time; nonamenable graphs; spectral gap", } @Article{Bordenave:2008:BAP, author = "Charles Bordenave", title = "On the birth-and-assassination process, with an application to scotching a rumor in a network", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "66:2014--66:2030", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-573", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/573", abstract = "We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has a heavy-tailed distribution. We also establish that this process is a scaling limit of a process of rumor scotching in a network, and is related to a predator-prey dynamics.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching process, heavy tail phenomena, SIR epidemics", } @Article{Neuenkirch:2008:DED, author = "Andreas Neuenkirch and Ivan Nourdin and Samy Tindel", title = "Delay equations driven by rough paths", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "67:2031--67:2068", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-575", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/575", abstract = "In this article, we illustrate the flexibility of the algebraic integration formalism introduced in M. Gubinelli, {\em J. Funct. Anal.} {\bf 216}, 86-140, 2004, \url{http://www.ams.org/mathscinet-getitem?mr=2005k:60169} Math. Review 2005k:60169, by establishing an existence and uniqueness result for delay equations driven by rough paths. We then apply our results to the case where the driving path is a fractional Brownian motion with Hurst parameter $ H > 1 / 3 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "delay equation; fractional Brownian motion; Malliavin calculus; rough paths theory", } @Article{Hermisson:2008:PGH, author = "Joachim Hermisson and Peter Pfaffelhuber", title = "The pattern of genetic hitchhiking under recurrent mutation", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "68:2069--68:2106", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-577", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/577", abstract = "Genetic hitchhiking describes evolution at a neutral locus that is linked to a selected locus. If a beneficial allele rises to fixation at the selected locus, a characteristic polymorphism pattern (so-called selective sweep) emerges at the neutral locus. The classical model assumes that fixation of the beneficial allele occurs from a single copy of this allele that arises by mutation. However, recent theory (Pennings and Hermisson, 2006a, b) has shown that recurrent beneficial mutation at biologically realistic rates can lead to markedly different polymorphism patterns, so-called soft selective sweeps. We extend an approach that has recently been developed for the classical hitchhiking model (Schweinsberg and Durrett, 2005; Etheridge et al., 2006) to study the recurrent mutation scenario. We show that the genealogy at the neutral locus can be approximated (to leading orders in the selection strength) by a marked Yule process with immigration. Using this formalism, we derive an improved analytical approximation for the expected heterozygosity at the neutral locus at the time of fixation of the beneficial allele.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Selective sweep, genetic hitchhiking, soft selective sweep, diffusion approximation, Yule process, random background", } @Article{Arguin:2008:CPS, author = "Louis-Pierre Arguin", title = "Competing Particle Systems and the {Ghirlanda--Guerra} Identities", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "69:2101--69:2117", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-579", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/579", abstract = "Competing particle systems are point processes on the real line whose configurations $X$ can be ordered decreasingly and evolve by increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and quantified by a matrix $ Q = \{ q_{ij} \} $. Quasi-stationary systems are those for which the law of $ (X, Q)$ is invariant under the evolution up to translation of $X$. It was conjectured by Aizenman and co-authors that the matrix $Q$ of robustly quasi-stationary systems must exhibit a hierarchical structure. This was established recently, up to a natural decomposition of the system, whenever the set $ S_Q$ of values assumed by $ q_{ij}$ is finite. In this paper, we study the general case where $ S_Q$ may be infinite. Using the past increments of the evolution, we show that the law of robustly quasi-stationary systems must obey the Ghirlanda--Guerra identities, which first appear in the study of spin glass models. This provides strong evidence that the above conjecture also holds in the general case. In addition, it yields an alternative proof of a theorem of Ruzmaikina and Aizenman for independent increments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Point processes, Ultrametricity, Ghirlanda--Guerra identities", } @Article{Garet:2008:FPC, author = "Olivier Garet and R{\'e}gine Marchand", title = "First-passage competition with different speeds: positive density for both species is impossible", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "70:2118--70:2159", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-581", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/581", abstract = "Consider two epidemics whose expansions on $ \mathbb {Z}^d $ are governed by two families of passage times that are distinct and stochastically comparable. We prove that when the weak infection survives, the space occupied by the strong one is almost impossible to detect. Particularly, in dimension two, we prove that one species finally occupies a set with full density, while the other one only occupies a set of null density. Furthermore, we observe the same fluctuations with respect to the asymptotic shape as for the weak infection evolving alone. By the way, we extend the H{\"a}ggstr{\"o}m-Pemantle non-coexistence result ``except perhaps for a denumerable set'' to families of stochastically comparable passage times indexed by a continuous parameter.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coexistence; competition; first-passage percolation; moderate deviations; random growth", } @Article{Athreya:2008:RDT, author = "Siva Athreya and Rahul Roy and Anish Sarkar", title = "Random directed trees and forest --- drainage networks with dependence", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "71:2160--71:2189", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-580", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/580", abstract = "Consider the $d$-dimensional lattice $ \mathbb Z^d$ where each vertex is `open' or `closed' with probability $p$ or $ 1 - p$ respectively. An open vertex $v$ is connected by an edge to the closest open vertex $ w$ in the $ 45^\circ $ (downward) light cone generated at $v$. In case of non-uniqueness of such a vertex $w$, we choose any one of the closest vertices with equal probability and independently of the other random mechanisms. It is shown that this random graph is a tree almost surely for $ d = 2$ and $3$ and it is an infinite collection of distinct trees for $ d \geq 4$. In addition, for any dimension, we show that there is no bi-infinite path in the tree.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random Graph, Random Oriented Trees, Random Walk", } @Article{Heunis:2008:ICN, author = "Andrew Heunis and Vladimir Lucic", title = "On the Innovations Conjecture of Nonlinear Filtering with Dependent Data", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "72:2190--72:2216", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-585", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/585", abstract = "We establish the innovations conjecture for a nonlinear filtering problem in which the signal to be estimated is conditioned by the observations. The approach uses only elementary stochastic analysis, together with a variant due to J. M. C. Clark of a theorem of Yamada and Watanabe on pathwise-uniqueness and strong solutions of stochastic differential equations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "innovations conjecture; nonlinear filter; pathwise-uniqueness", } @Article{Faggionato:2008:RWE, author = "Alessandra Faggionato", title = "Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "73:2217--73:2247", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-591", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/591", abstract = "We consider a stationary and ergodic random field $ \{ \omega (b) \colon b \in \mathbb {E}_d \} $ parameterized by the family of bonds in $ \mathbb {Z}^d $, $ d \geq 2 $. The random variable $ \omega (b) $ is thought of as the conductance of bond $b$ and it ranges in a finite interval $ [0, c_0]$. Assuming that the set of bonds with positive conductance has a unique infinite cluster $ \mathcal {C}(\omega)$, we prove homogenization results for the random walk among random conductances on $ \mathcal {C}(\omega)$. As a byproduct, applying the general criterion of Faggionato (2007) leading to the hydrodynamic limit of exclusion processes with bond--dependent transition rates, for almost all realizations of the environment we prove the hydrodynamic limit of simple exclusion processes among random conductances on $ \mathcal {C}(\omega)$. The hydrodynamic equation is given by a heat equation whose diffusion matrix does not depend on the environment. We do not require any ellipticity condition. As special case, $ \mathcal {C}(\omega)$ can be the infinite cluster of supercritical Bernoulli bond percolation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bond percolation; disordered system; exclusion process; homogenization; random walk in random environment", } @Article{Mueller:2008:RDS, author = "Carl Mueller and David Nualart", title = "Regularity of the density for the stochastic heat equation", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "74:2248--74:2258", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-589", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/589", abstract = "We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear heat equation with multiplicative white noise. Then we settle this question by proving that solutions to the linear equation have negative moments of all orders.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "heat equation, white noise, Malliavin calculus, stochastic partial differential equations", } @Article{Zemlys:2008:HFS, author = "Vaidotas Zemlys", title = "A {H{\"o}lderian} {FCLT} for some multiparameter summation process of independent non-identically distributed random variables", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "75:2259--75:2282", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-590", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/590", abstract = "We introduce a new construction of a summation process based on the collection of rectangular subsets of unit d-dimensional cube for a triangular array of independent non-identically distributed variables with d-dimensional index, using the non-uniform grid adapted to the variances of the variables. We investigate its convergence in distribution in some Holder spaces. It turns out that for dimensions greater than 2, the limiting process is not necessarily the standard Brownian sheet. This contrasts with a classical result of Prokhorov for the one-dimensional case.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian sheet, functional central limit theorem, H{\"o}lder space, invariance principle, triangular array, summation process.", } @Article{Drewitz:2008:LEO, author = "Alexander Drewitz", title = "{Lyapunov} exponents for the one-dimensional parabolic {Anderson} model with drift", journal = j-ELECTRON-J-PROBAB, volume = "13", pages = "76:2283--76:2336", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v13-586", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/586", abstract = "We consider the solution to the one-dimensional parabolic Anderson model with homogeneous initial condition, arbitrary drift and a time-independent potential bounded from above. Under ergodicity and independence conditions we derive representations for both the quenched Lyapunov exponent and, more importantly, the $p$-th annealed Lyapunov exponents for all positive real $p$. These results enable us to prove the heuristically plausible fact that the $p$-th annealed Lyapunov exponent converges to the quenched Lyapunov exponent as $p$ tends to 0. Furthermore, we show that the solution is $p$-intermittent for $p$ large enough. As a byproduct, we compute the optimal quenched speed of the random walk appearing in the Feynman--Kac representation of the solution under the corresponding Gibbs measure. In our context, depending on the negativity of the potential, a phase transition from zero speed to positive speed appears as the drift parameter or diffusion constant increase, respectively.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Parabolic Anderson model, Lyapunov exponents, intermittency, large deviations", } @Article{Hambly:2009:PHI, author = "Ben Hambly and Martin Barlow", title = "Parabolic {Harnack} inequality and local limit theorem for percolation clusters", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "1:1--1:26", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-587", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/587", abstract = "We consider the random walk on supercritical percolation clusters in $ \mathbb {Z}^d $. Previous papers have obtained Gaussian heat kernel bounds, and a.s. invariance principles for this process. We show how this information leads to a parabolic Harnack inequality, a local limit theorem and estimates on the Green's function.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Harnack inequality; local limit theorem; Percolation; random walk", } @Article{Douc:2009:FIC, author = "Randal Douc and Eric Moulines and Yaacov Ritov", title = "Forgetting of the initial condition for the filter in general state-space hidden {Markov} chain: a coupling approach", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "2:27--2:49", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-593", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/593", abstract = "We give simple conditions that ensure exponential forgetting of the initial conditions of the filter for general state-space hidden Markov chain. The proofs are based on the coupling argument applied to the posterior Markov kernels. These results are useful both for filtering hidden Markov models using approximation methods (e.g., particle filters) and for proving asymptotic properties of estimators. The results are general enough to cover models like the Gaussian state space model, without using the special structure that permits the application of the Kalman filter.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "hidden Markov chain; non-linear filtering, coupling; stability", } @Article{Atar:2009:ETG, author = "Rami Atar and Siva Athreya and Zhen-Qing Chen", title = "Exit Time, Green Function and Semilinear Elliptic Equations", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "3:50--3:71", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-597", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/597", abstract = "Let $D$ be a bounded Lipschitz domain in $ R^n$ with $ n \geq 2$ and $ \tau_D$ be the first exit time from $D$ by Brownian motion on $ R^n$. In the first part of this paper, we are concerned with sharp estimates on the expected exit time $ E_x [\tau_D]$. We show that if $D$ satisfies a uniform interior cone condition with angle $ \theta \in (\cos^{-1}(1 / \sqrt {n}), \pi)$, then $ c_1 \varphi_1 (x) \leq E_x [\tau_D] \leq c_2 \varphi_1 (x)$ on $D$. Here $ \varphi_1$ is the first positive eigenfunction for the Dirichlet Laplacian on $D$. The above result is sharp as we show that if $D$ is a truncated circular cone with angle $ \theta < \cos^{-1}(1 / \sqrt {n})$, then the upper bound for $ E_x [\tau_D]$ fails. These results are then used in the second part of this paper to investigate whether positive solutions of the semilinear equation $ \Delta u = u^p$ in $ D, $ $ p \in R$, that vanish on an open subset $ \Gamma \subset \partial D$ decay at the same rate as $ \varphi_1$ on $ \Gamma $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "boundary Harnack principle; Brownian motion; Dirichlet Laplacian; exit time; Feynman--Kac transform; Green function estimates; ground state; Lipschitz domain; Schauder's fixed point theorem; semilinear elliptic equation", } @Article{Ibarrola:2009:FTR, author = "Ricardo V{\'e}lez Ibarrola and Tomas Prieto-Rumeau", title = "{De Finetti}'s-type results for some families of non identically distributed random variables", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "4:72--4:86", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-602", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/602", abstract = "We consider random selection processes of weighted elements in an arbitrary set. Their conditional distributions are shown to be a generalization of the hypergeometric distribution, while the marginal distributions can always be chosen as generalized binomial distributions. Then we propose sufficient conditions on the weight function ensuring that the marginal distributions are necessarily of the generalized binomial form. In these cases, the corresponding indicator random variables are conditionally independent (as in the classical De Finetti theorem) though they are neither exchangeable nor identically distributed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "De Finetti theorem; exchangeability; random assignment processes", } @Article{Janson:2009:PRG, author = "Svante Janson", title = "On percolation in random graphs with given vertex degrees", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "5:86--5:118", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-603", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/603", abstract = "We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for random graphs with given vertex degrees. This is used to study existence of giant component and existence of k-core. As a variation of the latter, we study also bootstrap percolation in random regular graphs. We obtain both simple new proofs of known results and new results. An interesting feature is that for some degree sequences, there are several or even infinitely many phase transitions for the k-core.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bootstrap percolation; giant component; k-core; random graph", } @Article{Sega:2009:LRC, author = "Gregor Sega", title = "Large-range constant threshold growth model in one dimension", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "6:119--6:138", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-598", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/598", abstract = "We study a one dimensional constant threshold model in continuous time. Its dynamics have two parameters, the range $n$ and the threshold $v$. An unoccupied site $x$ becomes occupied at rate 1 as soon as there are at least $v$ occupied sites in $ [x - n, x + n]$. As n goes to infinity and $v$ is kept fixed, the dynamics can be approximated by a continuous space version, which has an explicit invariant measure at the front. This allows us to prove that the speed of propagation is asymptoticaly $ n^2 / 2 v$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "asymptotic propagation velocity; growth model; invariant distribution", } @Article{Weiss:2009:EBS, author = "Alexander Weiss", title = "Escaping the {Brownian} stalkers", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "7:139--7:160", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-594", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/594", abstract = "We propose a simple model for the behaviour of longterm investors on a stock market. It consists of three particles that represent the stock's current price and the buyers', respectively sellers', opinion about the right trading price. As time evolves, both groups of traders update their opinions with respect to the current price. The speed of updating is controlled by a parameter; the price process is described by a geometric Brownian motion. We consider the market's stability in terms of the distance between the buyers' and sellers' opinion, and prove that the distance process is recurrent/transient in dependence on the parameter.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "financial markets; market stability; recurrence; stochastic dynamics; transience", } @Article{Bovier:2009:ASS, author = "Anton Bovier and Anton Klimovsky", title = "The {Aizenman--Sims--Starr} and {Guerras} schemes for the {SK} model with multidimensional spins", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "8:161--8:241", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-611", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/611", abstract = "We prove upper and lower bounds on the free energy of the Sherrington--Kirkpatrick model with multidimensional spins in terms of variational inequalities. The bounds are based on a multidimensional extension of the Parisi functional. We generalise and unify the comparison scheme of Aizenman, Sims and Starr and the one of Guerra involving the GREM-inspired processes and Ruelle's probability cascades. For this purpose, an abstract quenched large deviations principle of the G{\"a}rtner-Ellis type is obtained. We derive Talagrand's representation of Guerra's remainder term for the Sherrington--Kirkpatrick model with multidimensional spins. The derivation is based on well-known properties of Ruelle's probability cascades and the Bolthausen--Sznitman coalescent. We study the properties of the multidimensional Parisi functional by establishing a link with a certain class of semi-linear partial differential equations. We embed the problem of strict convexity of the Parisi functional in a more general setting and prove the convexity in some particular cases which shed some light on the original convexity problem of Talagrand. Finally, we prove the Parisi formula for the local free energy in the case of multidimensional Gaussian a priori distribution of spins using Talagrand's methodology of a priori estimates.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Sherrington--Kirkpatrick model, multidimensional spins, quenched large deviations, concentration of measure, Gaussian spins, convexity, Parisi functional, Parisi formula", } @Article{Taylor:2009:CPS, author = "Jesse Taylor and Amandine V{\'e}ber", title = "Coalescent processes in subdivided populations subject to recurrent mass extinctions", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "9:242--9:288", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-595", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/595", abstract = "We investigate the infinitely many demes limit of the genealogy of a sample of individuals from a subdivided population that experiences sporadic mass extinction events. By exploiting a separation of time scales that occurs within a class of structured population models generalizing Wright's island model, we show that as the number of demes tends to infinity, the limiting form of the genealogy can be described in terms of the alternation of instantaneous scattering phases that depend mainly on local demographic processes, and extended collecting phases that are dominated by global processes. When extinction and recolonization events are local, the genealogy is described by Kingman's coalescent, and the scattering phase influences only the overall rate of the process. In contrast, if the demes left vacant by a mass extinction event are recolonized by individuals emerging from a small number of demes, then the limiting genealogy is a coalescent process with simultaneous multiple mergers (a $ \Xi $-coalescent). In this case, the details of the within-deme population dynamics influence not only the overall rate of the coalescent process, but also the statistics of the complex mergers that can occur within sample genealogies. These results suggest that the combined effects of geography and disturbance could play an important role in producing the unusual patterns of genetic variation documented in some marine organisms with high fecundity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "disturbance; extinction/recolonization; genealogy; metapopulation; population genetics; separation of time scales; Xi-coalescent", } @Article{Alsmeyer:2009:LTM, author = "Gerold Alsmeyer and Alex Iksanov", title = "A Log-Type Moment Result for Perpetuities and Its Application to Martingales in Supercritical Branching Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "10:289--10:313", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-596", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/596", abstract = "Infinite sums of i.i.d. random variables discounted by a multiplicative random walk are called perpetuities and have been studied by many authors. The present paper provides a log-type moment result for such random variables under minimal conditions which is then utilized for the study of related moments of a.s. limits of certain martingales associated with the supercritical branching random walk. The connection arises upon consideration of a size-biased version of the branching random walk originally introduced by Lyons. As a by-product, necessary and sufficient conditions for uniform integrability of these martingales are provided in the most general situation which particularly means that the classical (LlogL)-condition is not always needed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching random walk; martingale; moments; perpetuity", } @Article{Foondun:2009:HKE, author = "Mohammud Foondun", title = "Heat kernel estimates and {Harnack} inequalities for some {Dirichlet} forms with non-local part", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "11:314--11:340", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-604", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/604", abstract = "We consider the Dirichlet form given by\par $$ {\cal E}(f, f) = \frac {1}{2} \int_{R^d} \sum_{i, j = 1}^d a_{ij}(x) \frac {\partial f(x)}{\partial x_i} \frac {\partial f(x)}{\partial x_j} d x $$ $$ + \int_{R^d \times R^d} (f(y) - f(x))^2 J(x, y)d x d y. $$ Under the assumption that the $ {a_{ij}} $ are symmetric and uniformly elliptic and with suitable conditions on $J$, the nonlocal part, we obtain upper and lower bounds on the heat kernel of the Dirichlet form. We also prove a Harnack inequality and a regularity theorem for functions that are harmonic with respect to $ \cal E$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Integro-differential operators. Harnack inequality. Heat kernel, Holder continuity", } @Article{Lejay:2009:RDE, author = "Antoine Lejay", title = "On rough differential equations", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "12:341--12:364", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-613", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/613", abstract = "We prove that the It{\^o} map, that is the map that gives the solution of a differential equation controlled by a rough path of finite $p$-variation with $ p \in [2, 3)$ is locally Lipschitz continuous in all its arguments and we give some sufficient conditions for global existence for non-bounded vector fields.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Barbour:2009:SCI, author = "A. Barbour and A. Gnedin", title = "Small counts in the infinite occupancy scheme", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "13:365--13:384", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-608", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/608", abstract = "The paper is concerned with the classical occupancy scheme in which balls are thrown independently into infinitely many boxes, with given probability of hitting each of the boxes. We establish joint normal approximation, as the number of balls goes to infinity, for the numbers of boxes containing any fixed number of balls, standardized in the natural way, assuming only that the variances of these counts all tend to infinity. The proof of this approximation is based on a de-Poissonization lemma. We then review sufficient conditions for the variances to tend to infinity. Typically, the normal approximation does not mean convergence. We show that the convergence of the full vector of counts only holds under a condition of regular variation, thus giving a complete characterization of possible limit correlation structures.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "normal approximation; occupancy problem; Poissonization; regular variation", } @Article{Gravner:2009:LBP, author = "Janko Gravner and Alexander Holroyd", title = "Local Bootstrap Percolation", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "14:385--14:399", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-607", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/607", abstract = "We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single {\em active} site at the origin, while other sites of $ \mathbb {Z}^2 $ are independently {\em occupied} with small probability $p$, otherwise {\em empty}. Subsequently, an empty site becomes active by contact with two or more active neighbors, and an occupied site becomes active if it has an active site within distance 2. We prove that the entire lattice becomes active with probability $ \exp [\alpha (p) / p]$, where $ \alpha (p)$ is between $ - \pi^2 / 9 + c \sqrt p$ and $ - \pi^2 / 9 + C \sqrt p(\log p^{-1})^3$. This corrects previous numerical predictions for the scaling of the correction term.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bootstrap percolation; cellular automaton; crossover; finite-size scaling; metastability", } @Article{Chen:2009:NFM, author = "Bo Chen and Daniel Ford and Matthias Winkel", title = "A new family of {Markov} branching trees: the alpha-gamma model", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "15:400--15:430", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-616", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/616", abstract = "We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from Duquesne and Le Gall's stable continuum random tree. We call these new trees the alpha-gamma trees. In this paper, we obtain their splitting rules, dislocation measures both in ranked order and in size-biased order, and we study their limiting behaviour.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Alpha-gamma tree, splitting rule, sampling consistency, self-similar fragmentation, dislocation measure, continuum random tree, R-tree, Markov branching model", } @Article{Tournier:2009:IET, author = "Laurent Tournier", title = "Integrability of exit times and ballisticity for random walks in {Dirichlet} environment", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "16:431--16:451", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-609", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/609", abstract = "We consider random walks in Dirichlet random environment. Since the Dirichlet distribution is not uniformly elliptic, the annealed integrability of the exit time out of a given finite subset is a non-trivial question. In this paper we provide a simple and explicit equivalent condition for the integrability of Green functions and exit times on any finite directed graph. The proof relies on a quotienting procedure allowing for an induction argument on the cardinality of the graph. This integrability problem arises in the definition of Kalikow auxiliary random walk. Using a particular case of our condition, we prove a refined version of the ballisticity criterion given by Enriquez and Sabot.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "ballisticity; Dirichlet distribution; exit time; quotient graph; random walks in random environment; reinforced random walks", } @Article{Bryc:2009:DRQ, author = "W{\l}odek Bryc and Virgil Pierce", title = "Duality of real and quaternionic random matrices", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "17:452--17:476", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-606", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/606", abstract = "We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner and Wishart families of random matrices the result gives the duality between moments of these families and the corresponding real Wigner and Wishart families.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian Symplectic Ensemble, quaternion Wishart, moments, Mobius graphs, Euler characteristic", } @Article{Bahlali:2009:HSP, author = "Khaled Bahlali and A. Elouaflin and Etienne Pardoux", title = "Homogenization of semilinear {PDEs} with discontinuous averaged coefficients", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "18:477--18:499", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-627", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/627", abstract = "We study the asymptotic behavior of solutions of semilinear PDEs. Neither periodicity nor ergodicity will be assumed. On the other hand, we assume that the coefficients have averages in the Cesaro sense. In such a case, the averaged coefficients could be discontinuous. We use a probabilistic approach based on weak convergence of the associated backward stochastic dierential equation (BSDE) in the Jakubowski $S$-topology to derive the averaged PDE. However, since the averaged coefficients are discontinuous, the classical viscosity solution is not defined for the averaged PDE. We then use the notion of ``$ L_p$-viscosity solution'' introduced in [7]. The existence of $ L_p$-viscosity solution to the averaged PDE is proved here by using BSDEs techniques.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Backward stochastic differential equations (BSDEs), $L^p$-viscosity solution for PDEs, homogenization, Jakubowski S-topology, limit in the Cesaro sense", } @Article{Denis:2009:MPC, author = "Laurent Denis and Anis Matoussi and Lucretiu Stoica", title = "Maximum Principle and Comparison Theorem for Quasi-linear Stochastic {PDE}'s", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "19:500--19:530", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-629", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/629", abstract = "We prove a comparison theorem and maximum principle for a local solution of quasi-linear parabolic stochastic PDEs, similar to the well known results in the deterministic case. The proofs are based on a version of It{\^o}'s formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary. Moreover we shortly indicate how these results generalize for Burgers type SPDEs", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic partial differential equation, It{\^o}'s formula, Maximum principle, Moser's iteration", } @Article{Toninelli:2009:CGF, author = "Fabio Toninelli", title = "Coarse graining, fractional moments and the critical slope of random copolymers", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "20:531--20:547", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-612", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/612", abstract = "For a much-studied model of random copolymer at a selective interface we prove that the slope of the critical curve in the weak-disorder limit is strictly smaller than 1, which is the value given by the annealed inequality. The proof is based on a coarse-graining procedure, combined with upper bounds on the fractional moments of the partition function.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Coarse-graining; Copolymers at Selective Interfaces; Fractional Moment Estimates", } @Article{Foondun:2009:INP, author = "Mohammud Foondun and Davar Khoshnevisan", title = "Intermittence and nonlinear parabolic stochastic partial differential equations", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "21:548--21:568", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-614", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/614", abstract = "We consider nonlinear parabolic SPDEs of the form $ \partial_t u = {\cal L} u + \sigma (u) \dot w $, where $ \dot w $ denotes space-time white noise, $ \sigma \colon R \to R $ is [globally] Lipschitz continuous, and $ \cal L $ is the $ L^2$-generator of a L'evy process. We present precise criteria for existence as well as uniqueness of solutions. More significantly, we prove that these solutions grow in time with at most a precise exponential rate. We establish also that when $ \sigma $ is globally Lipschitz and asymptotically sublinear, the solution to the nonlinear heat equation is ``weakly intermittent, '' provided that the symmetrization of $ \cal L$ is recurrent and the initial data is sufficiently large. Among other things, our results lead to general formulas for the upper second-moment Liapounov exponent of the parabolic Anderson model for $ \cal L$ in dimension $ (1 + 1)$. When $ {\cal L} = \kappa \partial_{xx}$ for $ \kappa > 0$, these formulas agree with the earlier results of statistical physics (Kardar (1987), Krug and Spohn (1991), Lieb and Liniger (1963)), and also probability theory (Bertini and Cancrini (1995), Carmona and Molchanov (1994)) in the two exactly-solvable cases. That is when $ u_0 = \delta_0$ or $ u_0 \equiv 1$; in those cases the moments of the solution to the SPDE can be computed (Bertini and Cancrini (1995)).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic partial differential equations, Levy processes", } @Article{Gantert:2009:STR, author = "Nina Gantert and Serguei Popov and Marina Vachkovskaia", title = "Survival time of random walk in random environment among soft obstacles", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "22:569--22:593", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-631", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/631", abstract = "We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d. random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain quenched and annealed bounds on the tails of the survival time in the general $d$-dimensional case. We then consider a simplified one-dimensional model (where transition probabilities and obstacles are independent and the RWRE only moves to neighbour sites), and obtain finer results for the tail of the survival time. In addition, we study also the ``mixed'' probability measures (quenched with respect to the obstacles and annealed with respect to the transition probabilities and vice-versa) and give results for tails of the survival time with respect to these probability measures. Further, we apply the same methods to obtain bounds for the tails of hitting times of Branching Random Walks in Random Environment (BRWRE).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "confinement of RWRE, survival time, quenched and annealed tails, nestling RWRE, branching random walks in random environment", } @Article{Matsui:2009:EFO, author = "Muneya Matsui and Narn-Rueih Shieh", title = "On the Exponentials of Fractional {Ornstein--Uhlenbeck} Processes", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "23:594--23:611", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-628", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/628", abstract = "We study the correlation decay and the expected maximal increment (Burkholder--Davis--Gundy type inequalities) of the exponential process determined by a fractional Ornstein--Uhlenbeck process. The method is to apply integration by parts formula on integral representations of fractional Ornstein--Uhlenbeck processes, and also to use Slepian's inequality. As an application, we attempt Kahane's T-martingale theory based on our exponential process which is shown to be of long memory.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Long memory (Long range dependence), Fractional Brownian motion, Fractional Ornstein--Uhlenbeck process, Exponential process, Burkholder--Davis--Gundy inequalities", } @Article{Chassagneux:2009:RCL, author = "Jean-Fran{\c{c}}ois Chassagneux and Bruno Bouchard", title = "Representation of continuous linear forms on the set of ladlag processes and the hedging of {American} claims under proportional costs", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "24:612--24:632", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-625", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/625", abstract = "We discuss a d-dimensional version (for l{\`a}dl{\`a}g optional processes) of a duality result by Meyer (1976) between {bounded} c{\`a}dl{\`a}g adapted processes and random measures. We show that it allows to establish, in a very natural way, a dual representation for the set of initial endowments which allow to super-hedge a given American claim in a continuous time model with proportional transaction costs. It generalizes a previous result of Bouchard and Temam (2005) who considered a discrete time setting. It also completes the very recent work of Denis, De Valli{\`e}re and Kabanov (2008) who studied c{\`a}dl{\`a}g American claims and used a completely different approach.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "American options; Randomized stopping times; transaction costs", } @Article{Kuwada:2009:CMM, author = "Kazumasa Kuwada", title = "Characterization of maximal {Markovian} couplings for diffusion processes", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "25:633--25:662", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-634", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/634", abstract = "Necessary conditions for the existence of a maximal Markovian coupling of diffusion processes are studied. A sufficient condition described as a global symmetry of the processes is revealed to be necessary for the Brownian motion on a Riemannian homogeneous space. As a result, we find many examples of a diffusion process which admits no maximal Markovian coupling. As an application, we find a Markov chain which admits no maximal Markovian coupling for specified starting points.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Maximal coupling, Markovian coupling, diffusion process, Markov chain", } @Article{Pinelis:2009:OTV, author = "Iosif Pinelis", title = "Optimal two-value zero-mean disintegration of zero-mean random variables", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "26:663--26:727", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-633", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/633", abstract = "For any continuous zero-mean random variable $X$, a reciprocating function $r$ is constructed, based only on the distribution of $X$, such that the conditional distribution of $X$ given the (at-most-)two-point set $ \{ X, r(X) \} $ is the zero-mean distribution on this set; in fact, a more general construction without the continuity assumption is given in this paper, as well as a large variety of other related results, including characterizations of the reciprocating function and modeling distribution asymmetry patterns. The mentioned disintegration of zero-mean r.v.'s implies, in particular, that an arbitrary zero-mean distribution is represented as the mixture of two-point zero-mean distributions; moreover, this mixture representation is most symmetric in a variety of senses. Somewhat similar representations - of any probability distribution as the mixture of two-point distributions with the same skewness coefficient (but possibly with different means) - go back to Kolmogorov; very recently, Aizenman et al. further developed such representations and applied them to (anti-)concentration inequalities for functions of independent random variables and to spectral localization for random Schroedinger operators. One kind of application given in the present paper is to construct certain statistical tests for asymmetry patterns and for location without symmetry conditions. Exact inequalities implying conservative properties of such tests are presented. These developments extend results established earlier by Efron, Eaton, and Pinelis under a symmetry condition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Disintegration of measures, Wasserstein metric, Kantorovich-Rubinstein theorem, transportation of measures, optimal matching, most symmetric, hypothesis testing, confidence regions, Student's t-test, asymmetry, exact inequalities, conservative properties", } @Article{Shkolnikov:2009:CPS, author = "Mykhaylo Shkolnikov", title = "Competing Particle Systems Evolving by {I.I.D.} Increments", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "27:728--27:751", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-635", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/635", abstract = "We consider competing particle systems in $ \mathbb {R}^d $, i.e., random locally finite upper bounded configurations of points in $ \mathbb {R}^d $ evolving in discrete time steps. In each step i.i.d. increments are added to the particles independently of the initial configuration and the previous steps. Ruzmaikina and Aizenman characterized quasi-stationary measures of such an evolution, i.e., point processes for which the joint distribution of the gaps between the particles is invariant under the evolution, in case $ d = 1 $ and restricting to increments having a density and an everywhere finite moment generating function. We prove corresponding versions of their theorem in dimension $ d = 1 $ for heavy-tailed increments in the domain of attraction of a stable law and in dimension $ d \geq 1 $ for lattice type increments with an everywhere finite moment generating function. In all cases we only assume that under the initial configuration no two particles are located at the same point. In addition, we analyze the attractivity of quasi-stationary Poisson point processes in the space of all Poisson point processes with almost surely infinite, locally finite and upper bounded configurations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Competing particle systems, Large deviations, Spin glasses", } @Article{Delyon:2009:EIS, author = "Bernard Delyon", title = "Exponential inequalities for sums of weakly dependent variables", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "28:752--28:779", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-636", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/636", abstract = "We give new exponential inequalities and Gaussian approximation results for sums of weakly dependent variables. These results lead to generalizations of Bernstein and Hoeffding inequalities, where an extra control term is added; this term contains conditional moments of the variables.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Mixing, exponential inequality; random fields; weak dependence", } @Article{Woodard:2009:SCT, author = "Dawn Woodard and Scott Schmidler and Mark Huber", title = "Sufficient Conditions for Torpid Mixing of Parallel and Simulated Tempering", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "29:780--29:804", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-638", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/638", abstract = "We obtain upper bounds on the spectral gap of Markov chains constructed by parallel and simulated tempering, and provide a set of sufficient conditions for torpid mixing of both techniques. Combined with the results of Woodard, Schmidler and Huber (2009), these results yield a two-sided bound on the spectral gap of these algorithms. We identify a persistence property of the target distribution, and show that it can lead unexpectedly to slow mixing that commonly used convergence diagnostics will fail to detect. For a multimodal distribution, the persistence is a measure of how ``spiky'', or tall and narrow, one peak is relative to the other peaks of the distribution. We show that this persistence phenomenon can be used to explain the torpid mixing of parallel and simulated tempering on the ferromagnetic mean-field Potts model shown previously. We also illustrate how it causes torpid mixing of tempering on a mixture of normal distributions with unequal covariances in $ R^M $, a previously unknown result with relevance to statistical inference problems. More generally, anytime a multimodal distribution includes both very narrow and very wide peaks of comparable probability mass, parallel and simulated tempering are shown to mix slowly.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov chain, rapid mixing, spectral gap, Metropolis algorithm", } @Article{Schertzer:2009:SPB, author = "Emmanuel Schertzer and Rongfeng Sun and Jan Swart", title = "Special points of the {Brownian} net", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "30:805--30:864", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-641", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/641", abstract = "The Brownian net, which has recently been introduced by Sun and Swart [16], and independently by Newman, Ravishankar and Schertzer [13], generalizes the Brownian web by allowing branching. In this paper, we study the structure of the Brownian net in more detail. In particular, we give an almost sure classification of each point in $ \mathbb {R}^2 $ according to the configuration of the Brownian net paths entering and leaving the point. Along the way, we establish various other structural properties of the Brownian net.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching-coalescing point set.; Brownian net; Brownian web", } @Article{Caballero:2009:ABI, author = "Mar{\'\i}a Caballero and V{\'\i}ctor Rivero", title = "On the asymptotic behaviour of increasing self-similar {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "31:865--31:894", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-637", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/637", abstract = "It has been proved by Bertoin and Caballero {citeBC2002} that a $ 1 / \alpha $-increasing self-similar Markov process $X$ is such that $ t^{-1 / \alpha }X(t)$ converges weakly, as $ t \to \infty, $ to a degenerate random variable whenever the subordinator associated to it via Lamperti's transformation has infinite mean. Here we prove that $ \log (X(t) / t^{1 / \alpha }) / \log (t)$ converges in law to a non-degenerate random variable if and only if the associated subordinator has Laplace exponent that varies regularly at $ 0.$ Moreover, we show that $ \liminf_{t \to \infty } \log (X(t)) / \log (t) = 1 / \alpha, $ a.s. and provide an integral test for the upper functions of $ \{ \log (X(t)), t \geq 0 \} $. Furthermore, results concerning the rate of growth of the random clock appearing in Lamperti's transformation are obtained. In particular, these allow us to establish estimates for the left tail of some exponential functionals of subordinators. Finally, some of the implications of these results in the theory of self-similar fragmentations are discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "self-similar Markov processes", } @Article{Meester:2009:USD, author = "Ronald Meester and Anne Fey-den Boer and Haiyan Liu", title = "Uniqueness of the stationary distribution and stabilizability in {Zhang}'s sandpile model", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "32:895--32:911", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-640", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/640", abstract = "We show that Zhang's sandpile model $ (N, [a, b]) $ on $N$ sites and with uniform additions on $ [a, b]$ has a unique stationary measure for all $ 0 \leq a < b \leq 1$. This generalizes earlier results of {citeanne} where this was shown in some special cases. We define the infinite volume Zhang's sandpile model in dimension $ d \geq 1$, in which topplings occur according to a Markov toppling process, and we study the stabilizability of initial configurations chosen according to some measure $ m u$. We show that for a stationary ergodic measure $ \mu $ with density $ \rho $, for all $ \rho < \frac {1}{2}$, $ \mu $ is stabilizable; for all $ \rho \geq 1$, $ \mu $ is not stabilizable; for $ \frac {1}{2} \leq \rho < 1$, when $ \rho $ is near to $ \frac {1}{2}$ or $1$, both possibilities can occur.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Sandpile, stationary distribution, coupling, critical density, stabilizability", } @Article{Appleby:2009:SSD, author = "John Appleby and Huizhong Wu", title = "Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm, with applications to financial markets", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "33:912--33:959", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-642", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/642", abstract = "By using a change of scale and space, we study a class of stochastic differential equations (SDEs) whose solutions are drift--perturbed and exhibit asymptotic behaviour similar to standard Brownian motion. In particular sufficient conditions ensuring that these processes obey the Law of the Iterated Logarithm (LIL) are given. Ergodic--type theorems on the average growth of these non-stationary processes, which also depend on the asymptotic behaviour of the drift coefficient, are investigated. We apply these results to inefficient financial market models. The techniques extend to certain classes of finite--dimensional equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; inefficient market; Law of the Iterated Logarithm; Motoo's theorem; stationary processes; stochastic comparison principle; stochastic differential equations", } @Article{Nagahata:2009:CLT, author = "Yukio Nagahata and Nobuo Yoshida", title = "{Central Limit Theorem} for a Class of Linear Systems", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "34:960--34:977", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-644", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/644", abstract = "We consider a class of interacting particle systems with values in $ [0, \infty)^{\mathbb {Z}^d} $, of which the binary contact path process is an example. For $ d \geq 3 $ and under a certain square integrability condition on the total number of the particles, we prove a central limit theorem for the density of the particles, together with upper bounds for the density of the most populated site and the replica overlap.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem, linear systems, binary contact path process, diffusive behavior, delocalization", } @Article{Dedecker:2009:RCM, author = "J{\'e}r{\^o}me Dedecker and Florence Merlev{\`e}de and Emmanuel Rio", title = "Rates of convergence for minimal distances in the central limit theorem underprojective criteria", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "35:978--35:1011", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-648", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/648", abstract = "In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Minimal and ideal distances, rates of convergence, Martingale difference sequences", } @Article{Masson:2009:GEP, author = "Robert Masson", title = "The growth exponent for planar loop-erased random walk", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "36:1012--36:1073", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-651", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/651", abstract = "We give a new proof of a result of Kenyon that the growth exponent for loop-erased random walks in two dimensions is 5/4. The proof uses the convergence of LERW to Schramm--Loewner evolution with parameter 2, and is valid for irreducible bounded symmetric random walks on any two dimensional discrete lattice.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "loop-erased random walk; Random walk; Schramm--Loewner evolution", } @Article{Hambly:2009:ENV, author = "Ben Hambly and Lisa Jones", title = "Erratum to {``Number Variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric $ \alpha $-stable processes''}", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "37:1074--37:1079", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-658", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Hambly:2007:NVP}.", URL = "http://ejp.ejpecp.org/article/view/658", abstract = "In our original paper, we provide an expression for the variance of the counting functions associated with the spatial particle configurations formed by infinite systems of independent symmetric alpha-stable processes. The formula (2.3) of the original paper, is in fact the correct expression for the expected conditional number variance. This is equal to the full variance when L is a positive integer multiple of the parameter a but, in general, the full variance has an additional bounded fluctuating term. The main results of the paper still hold for the full variance itself, although some of the proofs require modification in order to incorporate this change.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Number variance, symmetric $\alpha$-stable processes, controlled variability, Gaussian fluctuations, functional limits, long memory, Gaussian processes, fractional Brownian motion", } @Article{Schuhmacher:2009:DED, author = "Dominic Schuhmacher", title = "Distance estimates for dependent thinnings of point processes with densities", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "38:1080--38:1116", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-643", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/643", abstract = "In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour--Brown distance $ d_2 $ between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization with a result based on Stein's method. In the present article we concentrate on point processes that have a density with respect to a Poisson process, for which we can apply a corresponding result directly without the detour of discretization. This enables us to obtain better and more natural bounds in the $ d_2$-metric, and for the first time also bounds in the stronger total variation metric. We give applications for thinning by covering with an independent Boolean model and ``Matern type I'' thinning of fairly general point processes. These applications give new insight into the respective models, and either generalize or improve earlier results.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Barbour--Brown distance; point process; point process density; Poisson process approximation; random field; Stein's method; thinning; total variation distance", } @Article{Hutzenthaler:2009:VIM, author = "Martin Hutzenthaler", title = "The {Virgin Island} Model", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "39:1117--39:1161", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-646", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/646", abstract = "A continuous mass population model with local competition is constructed where every emigrant colonizes an unpopulated island. The population founded by an emigrant is modeled as excursion from zero of an one-dimensional diffusion. With this excursion measure, we construct a process which we call Virgin Island Model. A necessary and sufficient condition for extinction of the total population is obtained for finite initial total mass.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching populations; Crump-Mode-Jagers process; excursion measure; extinction; general branching process; local competition; survival; Virgin Island Model", } @Article{Redig:2009:CIM, author = "Frank Redig and Jean Rene Chazottes", title = "Concentration inequalities for {Markov} processes via coupling", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "40:1162--40:1180", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-657", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/657", abstract = "We obtain moment and Gaussian bounds for general coordinate-wise Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the coupling time exists, then we obtain a variance inequality. If a moment of order $ 1 + a $ $ (a > 0) $ of the coupling time exists, then depending on the behavior of the stationary distribution, we obtain higher moment bounds. This immediately implies polynomial concentration inequalities. In the case that a moment of order $ 1 + a $ is finite, uniformly in the starting point of the coupling, we obtain a Gaussian bound. We illustrate the general results with house of cards processes, in which both uniform and non-uniform behavior of moments of the coupling time can occur.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "concentration inequalities, coupling, Markov processes", } @Article{Hu:2009:CTM, author = "Zhishui Hu and Qi-Man Shao and Qiying Wang", title = "Cram{\'e}r Type Moderate deviations for the Maximum of Self-normalized Sums", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "41:1181--41:1197", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-663", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/663", abstract = "Let $ \{ X, X_i, i \geq 1 \} $ be i.i.d. random variables, $ S_k $ be the partial sum and $ V_n^2 = \sum_{1 \leq i \leq n} X_i^2 $. Assume that $ E(X) = 0 $ and $ E(X^4) < \infty $. In this paper we discuss the moderate deviations of the maximum of the self-normalized sums. In particular, we prove that $ P(\max_{1 \leq k \leq n} S_k \geq x V_n) / (1 - \Phi (x)) \to 2 $ uniformly in $ x \in [0, o(n^{1 / 6})) $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Large deviation, moderate deviation, self-normalized maximal sum", } @Article{Luschgy:2009:EGP, author = "Harald Luschgy and Gilles Pag{\`e}s", title = "Expansions for {Gaussian} Processes and {Parseval} Frames", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "42:1198--42:1221", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-649", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/649", abstract = "We derive a precise link between series expansions of Gaussian random vectors in a Banach space and Parseval frames in their reproducing kernel Hilbert space. The results are applied to pathwise continuous Gaussian processes and a new optimal expansion for fractional Ornstein--Uhlenbeck processes is derived.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian process, series expansion, Parseval frame, optimal expansion, fractional Ornstein--Uhlenbeck process", } @Article{Dereich:2009:RNS, author = "Steffen Dereich and Peter M{\"o}rters", title = "Random networks with sublinear preferential attachment: Degree evolutions", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "43:1222--43:1267", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-647", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/647", abstract = "We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and then have a closer look at the temporal evolution of the degrees of individual vertices, which we describe in terms of large and moderate deviation principles. Using these results, we expose an interesting phase transition: in cases of strong preference of large degrees, eventually a single vertex emerges forever as vertex of maximal degree, whereas in cases of weak preference, the vertex of maximal degree is changing infinitely often. Loosely speaking, the transition between the two phases occurs in the case when a new edge is attached to an existing vertex with a probability proportional to the root of its current degree.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Barabasi-Albert model; degree distribution; dynamic random graphs; large deviation principle; maximal degree; moderate deviation principle; sublinear preferential attachment", } @Article{Joseph:2009:FQM, author = "Mathew Joseph", title = "Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "44:1268--44:1289", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-655", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/655", abstract = "We consider an i.i.d. random environment with a strong form of transience on the two dimensional integer lattice. Namely, the walk always moves forward in the y-direction. We prove an invariance principle for the quenched expected position of the random walk indexed by its level crossing times. We begin with a variation of the Martingale Central Limit Theorem. The main part of the paper checks the conditions of the theorem for our problem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem; Green function; invariance principle; random walk in random environment", } @Article{Rath:2009:ERR, author = "Balazs Rath and Balint Toth", title = "{Erd{\H{o}}s--R{\'e}nyi} random graphs $+$ forest fires $=$ self-organized criticality", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "45:1290--45:1327", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-653", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/653", abstract = "We modify the usual Erd{\H{o}}s--R{\'e}nyi random graph evolution by letting connected clusters 'burn down' (i.e., fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the system sticks to a permanent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "forest fire model, Erd{\H{o}}s--R{\'e}nyi random graph, Smoluchowski coagulation equations, self-organized criticality", } @Article{Bojdecki:2009:OTB, author = "Tomasz Bojdecki and Luis Gorostiza and Anna Talarczyk", title = "Occupation times of branching systems with initial inhomogeneous {Poisson} states and related superprocesses", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "46:1328--46:1371", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-665", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/665", abstract = "The $ (d, \alpha, \beta, \gamma)$-branching particle system consists of particles moving in $ \mathbb {R}^d$ according to a symmetric $ \alpha $-stable L{\'e}vy process $ (0 < \alpha \leq 2)$, splitting with a critical $ (1 + \beta)$-branching law $ (0 < \beta \leq 1)$, and starting from an inhomogeneous Poisson random measure with intensity measure $ \mu_\gamma (d x) = d x / (1 + |x|^\gamma), \gamma \geq 0$. By means of time rescaling $T$ and Poisson intensity measure $ H_T \mu_\gamma $, occupation time fluctuation limits for the system as $ T \to \infty $ have been obtained in two special cases: Lebesgue measure ($ \gamma = 0$, the homogeneous case), and finite measures $ (\gamma > d)$. In some cases $ H_T \equiv 1$ and in others $ H_T \to \infty $ as $ T \to \infty $ (high density systems). The limit processes are quite different for Lebesgue and for finite measures. Therefore the question arises of what kinds of limits can be obtained for Poisson intensity measures that are intermediate between Lebesgue measure and finite measures. In this paper the measures $ \mu_\gamma, \gamma \in (0, d]$, are used for investigating this question. Occupation time fluctuation limits are obtained which interpolate in some way between the two previous extreme cases. The limit processes depend on different arrangements of the parameters $ d, \alpha, \beta, \gamma $. There are two thresholds for the dimension $d$. The first one, $ d = \alpha / \beta + \gamma $, determines the need for high density or not in order to obtain non-trivial limits, and its relation with a.s. local extinction of the system is discussed. The second one, $ d = [\alpha (2 + \beta) - \gamma \vee \alpha] / \beta $ \ (if $ \gamma < d$), interpolates between the two extreme cases, and it is a critical dimension which separates different qualitative behaviors of the limit processes, in particular long-range dependence in ``low'' dimensions, and independent increments in ``high'' dimensions. In low dimensions the temporal part of the limit process is a new self-similar stable process which has two different long-range dependence regimes depending on relationships among the parameters. Related results for the corresponding $ (d, \alpha, \beta, \gamma)$-superprocess are also given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching particle system; limit theorem; long-range dependence; occupation time fluctuation; stable process; superprocess", } @Article{Picco:2009:ODR, author = "Pierre Picco and Enza Orlandi", title = "One-dimensional random field {Kac}'s model: weak large deviations principle", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "47:1372--47:1416", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-662", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/662", abstract = "We present a quenched weak large deviations principle for the Gibbs measures of a Random Field Kac Model (RFKM) in one dimension. The external random magnetic field is given by symmetrically distributed Bernouilli random variables. The results are valid for values of the temperature and magnitude of the field in the region where the free energy of the corresponding random Curie Weiss model has only two absolute minimizers. We give an explicit representation of the large deviation rate function and characterize its minimizers. We show that they are step functions taking two values, the two absolute minimizers of the free energy of the random Curie Weiss model. The points of discontinuity are described by a stationary renewal process related to the $h$-extrema of a bilateral Brownian motion studied by Neveu and Pitman, where $h$ depends on the temperature and magnitude of the random field. Our result is a complete characterization of the typical profiles of RFKM (the ground states) which was initiated in [2] and extended in [4].", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "phase transition, large deviations random walk, random environment, Kac potential", } @Article{Rosen:2009:ECP, author = "Jay Rosen and Michael Marcus", title = "Existence of a critical point for the infinite divisibility of squares of {Gaussian} vectors in {$ R^2 $} with non--zero mean", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "48:1417--48:1455", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-669", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/669", abstract = "Let $ G = (G_1, G_2) $ be a Gaussian vector in $ R^2 $ with $ E(G_1 G_2) \ne 0 $. Let $ c_1, c_2 \in R^1 $. A necessary and sufficient condition for the vector $ ((G_1 + c_1 \alpha)^2, (G_2 + c_2 \alpha)^2) $ to be infinitely divisible for all $ \alpha \in R^1 $ is that\par $$ \Gamma_{i, i} \ge \frac {c_i}{c_j} \Gamma_{i, j} > 0 \qquad \forall \, 1 \leq i \ne j \leq 2. \qquad (0.1) $$ In this paper we show that when (0.1) does not hold there exists an $ 0 < \alpha_0 < \infty $ such that $ ((G_1 + c_1 \alpha)^2, (G_2 + c_2 \alpha)^2) $ is infinitely divisible for all $ | \alpha | \leq \alpha_0 $ but not for any $ | \alpha | > \alpha_0 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "critical point.; Gaussian vectors; infinite divisibility", } @Article{Saloff-Coste:2009:MTI, author = "Laurent Saloff-Coste and Jessica Zuniga", title = "Merging for time inhomogeneous finite {Markov} chains, {Part I}: Singular values and stability", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "49:1456--49:1494", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-656", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/656", abstract = "We develop singular value techniques in the context of time inhomogeneous finite Markov chains with the goal of obtaining quantitative results concerning the asymptotic behavior of such chains. We introduce the notion of c-stability which can be viewed as a generalization of the case when a time inhomogeneous chain admits an invariant measure. We describe a number of examples where these techniques yield quantitative results concerning the merging of the distributions of the time inhomogeneous chain started at two arbitrary points.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Time inhomogeneous Markov chains, merging, singular value inequalities", } @Article{Dombry:2009:FAR, author = "Clement Dombry and Nadine Guillotin-Plantard", title = "A functional approach for random walks in random sceneries", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "50:1495--50:1512", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-659", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/659", abstract = "A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study separately the convergence of the walk and of the scenery: on the one hand, a general criterion for the convergence of the local time of the walk is provided, on the other hand, the convergence of the random measures associated with the scenery is studied. This functional approach is robust enough to recover many of the known results on RWRS as well as new ones, including the case of many walkers evolving in the same scenery.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Weak convergence, Random walk, Random scenery, Local time", } @Article{Sami:2009:LER, author = "Mustapha Sami", title = "Lower estimates for random walks on a class of amenable $p$-adic groups", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "51:1513--51:1531", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-667", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/667", abstract = "We give central lower estimates for the transition kernels corresponding to symmetric random walks on certain amenable p-adic groups.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$p$-adic groups; Random walk", } @Article{Baker:2009:BSM, author = "David Baker and Marc Yor", title = "A {Brownian} sheet martingale with the same marginals as the arithmetic average of geometric {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "52:1532--52:1540", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-674", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/674", abstract = "We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion is replaced by a stable subordinator.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Convex order, Brownian sheet, Asian option, Running average", } @Article{Bianchi:2009:SAM, author = "Alessandra Bianchi and Anton Bovier and Dmitry Ioffe", title = "Sharp asymptotics for metastability in the random field {Curie--Weiss} model", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "53:1541--53:1603", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-673", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/673", abstract = "In this paper we study the metastable behavior of one of the simplest disordered spin system, the random field Curie--Weiss model. We will show how the potential theoretic approach can be used to prove sharp estimates on capacities and metastable exit times also in the case when the distribution of the random field is continuous. Previous work was restricted to the case when the random field takes only finitely many values, which allowed the reduction to a finite dimensional problem using lumping techniques. Here we produce the first genuine sharp estimates in a context where entropy is important.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "capacity; disordered system; Glauber dynamics; metastability; potential theory", } @Article{Teixeira:2009:IPT, author = "Augusto Teixeira", title = "Interlacement percolation on transient weighted graphs", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "54:1604--54:1627", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-670", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/670", abstract = "In this article, we first extend the construction of random interlacements, introduced by A. S. Sznitman in [14], to the more general setting of transient weighted graphs. We prove the Harris-FKG inequality for this model and analyze some of its properties on specific classes of graphs. For the case of non-amenable graphs, we prove that the critical value $ u_* $ for the percolation of the vacant set is finite. We also prove that, once $ \mathcal {G} $ satisfies the isoperimetric inequality $ I S_6 $ (see (1.5)), $ u_* $ is positive for the product $ \mathcal {G} \times \mathbb {Z} $ (where we endow $ \mathbb {Z} $ with unit weights). When the graph under consideration is a tree, we are able to characterize the vacant cluster containing some fixed point in terms of a Bernoulli independent percolation process. For the specific case of regular trees, we obtain an explicit formula for the critical value $ u_* $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walks, random interlacements, percolation", } @Article{Basdevant:2009:RTM, author = "Anne-Laure Basdevant and Arvind Singh", title = "Recurrence and transience of a multi-excited random walk on a regular tree", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "55:1628--55:1669", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-672", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/672", abstract = "We study a model of multi-excited random walk on a regular tree which generalizes the models of the once excited random walk and the digging random walk introduced by Volkov (2003). We show the existence of a phase transition and provide a criterion for the recurrence/transience property of the walk. In particular, we prove that the asymptotic behaviour of the walk depends on the order of the excitations, which contrasts with the one dimensional setting studied by Zerner (2005). We also consider the limiting speed of the walk in the transient regime and conjecture that it is not a monotonic function of the environment.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Multi-excited random walk, self-interacting random walk, branching Markov chain", } @Article{Sznitman:2009:DRW, author = "Alain-Sol Sznitman", title = "On the domination of a random walk on a discrete cylinder by random interlacements", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "56:1670--56:1704", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-679", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/679", abstract = "We consider simple random walk on a discrete cylinder with base a large $d$-dimensional torus of side-length $N$, when $d$ is two or more. We develop a stochastic domination control on the local picture left by the random walk in boxes of side-length almost of order $N$, at certain random times comparable to the square of the number of sites in the base. We show a domination control in terms of the trace left in similar boxes by random interlacements in the infinite $ (d + 1)$-dimensional cubic lattice at a suitably adjusted level. As an application we derive a lower bound on the disconnection time of the discrete cylinder, which as a by-product shows the tightness of the laws of the ratio of the square of the number of sites in the base to the disconnection time. This fact had previously only been established when $d$ is at least 17.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "disconnection; discrete cylinders; random interlacements; random walks", } @Article{Merkl:2009:SBC, author = "Franz Merkl and Silke Rolles", title = "Spontaneous breaking of continuous rotational symmetry in two dimensions", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "57:1705--57:1726", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-671", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/671", abstract = "In this article, we consider a simple model in equilibrium statistical mechanics for a two-dimensional crystal without defects. In this model, the local specifications for infinite-volume Gibbs measures are rotationally symmetric. We show that at sufficiently low, but positive temperature, rotational symmetry is spontaneously broken in some infinite-volume Gibbs measures.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gibbs measure, rotation, spontaneous symmetry breaking, continuous symmetry", } @Article{deBouard:2009:SDK, author = "Anne de Bouard and Arnaud Debussche", title = "Soliton dynamics for the {Korteweg--de Vries} equation with multiplicative homogeneous noise", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "58:1727--58:1744", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-683", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/683", abstract = "We consider a randomly perturbed Korteweg-de Vries equation. The perturbation is a random potential depending both on space and time, with a white noise behavior in time, and a regular, but stationary behavior in space. We investigate the dynamics of the soliton of the KdV equation in the presence of this random perturbation, assuming that the amplitude of the perturbation is small. We estimate precisely the exit time of the perturbed solution from a neighborhood of the modulated soliton, and we obtain the modulation equations for the soliton parameters. We moreover prove a central limit theorem for the dispersive part of the solution, and investigate the asymptotic behavior in time of the limit process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Korteweg-de Vries equation; solitary waves; stochastic partial differential equations; white noise, central limit theorem", } @Article{Warren:2009:SED, author = "Jon Warren and Peter Windridge", title = "Some examples of dynamics for {Gelfand--Tsetlin} patterns", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "59:1745--59:1769", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-682", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/682", abstract = "We give three examples of stochastic processes in the Gelfand--Tsetlin cone in which each component evolves independently apart from a blocking and pushing interaction. These processes give rise to couplings between certain conditioned Markov processes, last passage times and exclusion processes. In the first two examples, we deduce known identities in distribution between such processes whilst in the third example, the components of the process cannot escape past a wall at the origin and we obtain a new relation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "conditioned Markov process; exclusion process; Gelfand--Tsetlin cone; last passage percolation; random matrices", } @Article{Raimond:2009:SGR, author = "Olivier Raimond and Bruno Schapira", title = "On some generalized reinforced random walk on integers", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "60:1770--60:1789", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-685", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/685", abstract = "We consider Reinforced Random Walks where transitions probabilities are a function of the proportions of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to Pemantle [7] on trees", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Reinforced random walks, urn processes", } @Article{Beghin:2009:FPP, author = "Luisa Beghin and Enzo Orsingher", title = "Fractional {Poisson} processes and related planar random motions", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "61:1790--61:1826", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-675", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/675", abstract = "We present three different fractional versions of the Poisson process and some related results concerning the distribution of order statistics and the compound Poisson process. The main version is constructed by considering the difference-differential equation governing the distribution of the standard Poisson process, $ N(t), t > 0 $, and by replacing the time-derivative with the fractional Dzerbayshan--Caputo derivative of order $ \nu \in (0, 1] $. For this process, denoted by $ \mathcal {N}_\nu (t), t > 0, $ we obtain an interesting probabilistic representation in terms of a composition of the standard Poisson process with a random time, of the form $ \mathcal {N}_\nu (t) = N(\mathcal {T}_{2 \nu }(t)), $ $ t > 0 $. The time argument $ \mathcal {T}_{2 \nu }(t), t > 0 $, is itself a random process whose distribution is related to the fractional diffusion equation. We also construct a planar random motion described by a particle moving at finite velocity and changing direction at times spaced by the fractional Poisson process $ \mathcal {N}_\nu . $ For this model we obtain the distributions of the random vector representing the position at time $t$, under the condition of a fixed number of events and in the unconditional case. For some specific values of $ \nu \in (0, 1]$ we show that the random position has a Brownian behavior (for $ \nu = 1 / 2$) or a cylindrical-wave structure (for $ \nu = 1$).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Compound Poisson process; Cylindrical waves; Finite velocity random motions; Fractional derivative; Fractional heat-wave equations; Mittag-Leffler function; Order statistics; Random velocity motions", } @Article{Ethier:2009:LTP, author = "S. Ethier and Jiyeon Lee", title = "Limit theorems for {Parrondo}'s paradox", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "62:1827--62:1862", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-684", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/684", abstract = "That there exist two losing games that can be combined, either by random mixture or by nonrandom alternation, to form a winning game is known as Parrondo's paradox. We establish a strong law of large numbers and a central limit theorem for the Parrondo player's sequence of profits, both in a one-parameter family of capital-dependent games and in a two-parameter family of history-dependent games, with the potentially winning game being either a random mixture or a nonrandom pattern of the two losing games. We derive formulas for the mean and variance parameters of the central limit theorem in nearly all such scenarios; formulas for the mean permit an analysis of when the Parrondo effect is present.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Parrondo's paradox, Markov chain, strong law of large numbers, central limit theorem, strong mixing property, fundamental matrix, spectral representation", } @Article{Crisan:2009:NFS, author = "Dan Crisan and Michael Kouritzin and Jie Xiong", title = "Nonlinear filtering with signal dependent observation noise", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "63:1863--63:1883", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-687", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/687", abstract = "The paper studies the filtering problem for a non-classical framework: we assume that the observation equation is driven by a signal dependent noise. We show that the support of the conditional distribution of the signal is on the corresponding level set of the derivative of the quadratic variation process. Depending on the intrinsic dimension of the noise, we distinguish two cases: In the first case, the conditional distribution has discrete support and we deduce an explicit representation for the conditional distribution. In the second case, the filtering problem is equivalent to a classical one defined on a manifold and we deduce the evolution equation of the conditional distribution. The results are applied to the filtering problem where the observation noise is an Ornstein--Uhlenbeck process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Nonlinear Filtering, Ornstein Uhlenbeck Noise, Signal-", } @Article{Boucheron:2009:CSB, author = "Stephane Boucheron and Gabor Lugosi and Pascal Massart", title = "On concentration of self-bounding functions", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "64:1884--64:1899", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-690", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/690", abstract = "We prove some new concentration inequalities for self-bounding functions using the entropy method. As an application, we recover Talagrand's convex distance inequality. The new Bernstein-like inequalities for self-bounding functions are derived thanks to a careful analysis of the so-called Herbst argument. The latter involves comparison results between solutions of differential inequalities that may be interesting in their own right.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "concentration inequality, convex distance, self-bounding function", } @Article{Gao:2009:MDL, author = "Fuqing Gao and Yanqing Wang", title = "Moderate deviations and laws of the iterated logarithm for the volume of the intersections of {Wiener} sausages", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "65:1900--65:1935", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-692", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/692", abstract = "Using the high moment method and the Feynman--Kac semigroup technique, we obtain moderate deviations and laws of the iterated logarithm for the volume of the intersections of two and three dimensional Wiener sausages.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "large deviations; laws of the iterated logarithm; moderate deviations; Wiener sausage", } @Article{Collevecchio:2009:LTV, author = "Andrea Collevecchio", title = "Limit theorems for vertex-reinforced jump processes on regular trees", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "66:1936--66:1962", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-693", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/693", abstract = "Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly $b$ children, with $ b \geq 3$. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the root. Notice that it is still unknown if vertex-reinforced jump process is transient on the binary tree.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem; Reinforced random walks; strong law of large numbers", } @Article{Salminen:2009:SLM, author = "Paavo Salminen and Pierre Vallois", title = "On subexponentiality of the {L{\'e}vy} measure of the inverse local time; with applications to penalizations", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "67:1963--67:1991", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-686", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/686", abstract = "For a recurrent linear diffusion on the positive real axis we study the asymptotics of the distribution of its local time at 0 as the time parameter tends to infinity. Under the assumption that the L{\'e}vy measure of the inverse local time is subexponential this distribution behaves asymptotically as a multiple of the L{\'e}vy measure. Using spectral representations we find the exact value of the multiple. For this we also need a result on the asymptotic behavior of the convolution of a subexponential distribution and an arbitrary distribution on the positive real axis. The exact knowledge of the asymptotic behavior of the distribution of the local time allows us to analyze the process derived via a penalization procedure with the local time. This result generalizes the penalizations obtained by Roynette, Vallois and Yor in Studia Sci. Math. Hungar. 45(1), 2008 for Bessel processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, Bessel process, Hitting time, Tauberian theorem, excursions", } @Article{Aurzada:2009:SDP, author = "Frank Aurzada and Mikhail Lifshits", title = "On the small deviation problem for some iterated processes", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "68:1992--68:2010", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-689", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/689", abstract = "We derive general results on the small deviation behavior for some classes of iterated processes. This allows us, in particular, to calculate the rate of the small deviations for n-iterated Brownian motions and, more generally, for the iteration of n fractional Brownian motions. We also give a new and correct proof of some results in E. Nane, Electron. J. Probab. 11 (2006), no. 18, 434--459.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "iterated Brownian motion; iterated fractional Brownian motion; iterated process; local time; small ball problem; small deviations", } @Article{Spiliopoulos:2009:WPR, author = "Konstantinos Spiliopoulos", title = "{Wiener} Process with Reflection in Non-Smooth Narrow Tubes", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "69:2011--69:2037", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-691", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/691", abstract = "Wiener process with instantaneous reflection in narrow tubes of width $ \epsilon \ll 1 $ around axis $x$ is considered in this paper. The tube is assumed to be (asymptotically) non-smooth in the following sense. Let $ V^{\epsilon }(x)$ be the volume of the cross-section of the tube. We assume that $ \frac {1}{\epsilon }V^{\epsilon }(x)$ converges in an appropriate sense to a non-smooth function as $ \epsilon \downarrow 0$. This limiting function can be composed by smooth functions, step functions and also the Dirac delta distribution. Under this assumption we prove that the $x$-component of the Wiener process converges weakly to a Markov process that behaves like a standard diffusion process away from the points of discontinuity and has to satisfy certain gluing conditions at the points of discontinuity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Delay; Gluing Conditions; Narrow Tubes; Non-smooth Boundary; Reflection; Wiener Process", } @Article{Caravenna:2009:DPM, author = "Francesco Caravenna and Nicolas P{\'e}tr{\'e}lis", title = "Depinning of a polymer in a multi-interface medium", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "70:2038--70:2067", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-698", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/698", abstract = "In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is denoted by $ T = T_N $ and is allowed to grow with the size $N$ of the polymer. When the polymer receives a positive reward for touching the interfaces, its asymptotic behavior has been derived in Caravenna and Petrelis (2009), showing that a transition occurs when $ T_N \approx \log N$. In the present paper, we deal with the so-called {\em depinning case}, i.e., the polymer is repelled rather than attracted by the interfaces. Using techniques from renewal theory, we determine the scaling behavior of the model for large $N$ as a function of $ \{ T_N \}_N$, showing that two transitions occur, when $ T_N \approx N^{1 / 3}$ and when $ T_N \approx \sqrt {N}$ respectively.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Localization/delocalization transition; Pinning Model; Polymer Model; Random Walk; Renewal Theory", } @Article{Fradelizi:2009:CIC, author = "Matthieu Fradelizi", title = "Concentration inequalities for $s$-concave measures of dilations of {Borel} sets and applications", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "71:2068--71:2090", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-695", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/695", abstract = "We prove a sharp inequality conjectured by Bobkov on the measure of dilations of Borel sets in the Euclidean space by a $s$-concave probability measure. Our result gives a common generalization of an inequality of Nazarov, Sodin and Volberg and a concentration inequality of Gu{\'e}don. Applying our inequality to the level sets of functions satisfying a Remez type inequality, we deduce, as it is classical, that these functions enjoy dimension free distribution inequalities and Kahane--Khintchine type inequalities with positive and negative exponent, with respect to an arbitrary $s$-concave probability measure", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "dilation; Khintchine type inequalities; large deviations; localization lemma; log-concave measures; Remez type inequalities; small deviations; sublevel sets", } @Article{Gartner:2009:ICT, author = "J{\"u}rgen G{\"a}rtner and Frank den Hollander and Gr{\'e}gory Maillard", title = "Intermittency on catalysts: three-dimensional simple symmetric exclusion", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "72:2091--72:2129", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-694", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/694", abstract = "We continue our study of intermittency for the parabolic Anderson model $ \partial u / \partial t = \kappa \Delta u + \xi u $ in a space-time random medium $ \xi $, where $ \kappa $ is a positive diffusion constant, $ \Delta $ is the lattice Laplacian on $ \mathbb {Z}^d $, $ d \geq 1 $, and $ \xi $ is a simple symmetric exclusion process on $ \mathbb {Z}^d $ in Bernoulli equilibrium. This model describes the evolution of a {\em reactant} $u$ under the influence of a {\em catalyst} $ \xi $.\par In G{\"a}rtner, den Hollander and Maillard [3] we investigated the behavior of the annealed Lyapunov exponents, i.e., the exponential growth rates as $ t \to \infty $ of the successive moments of the solution $u$. This led to an almost complete picture of intermittency as a function of $d$ and $ \kappa $. In the present paper we finish our study by focussing on the asymptotics of the Lyaponov exponents as $ \kappa \to \infty $ in the {\em critical} dimension $ d = 3$, which was left open in G{\"a}rtner, den Hollander and Maillard [3] and which is the most challenging. We show that, interestingly, this asymptotics is characterized not only by a {\em Green} term, as in $ d \geq 4$, but also by a {\em polaron} term. The presence of the latter implies intermittency of {\em all} orders above a finite threshold for $ \kappa $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "catalytic random medium; exclusion process; graphical representation; intermittency; large deviations; Lyapunov exponents; Parabolic Anderson model", } @Article{Bercu:2009:FCL, author = "Bernard Bercu and Pierre {Del Moral} and Arnaud Doucet", title = "A Functional {Central Limit Theorem} for a Class of Interacting {Markov} Chain {Monte Carlo} Methods", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "73:2130--73:2155", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-701", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/701", abstract = "We present a functional central limit theorem for a new class of interacting Markov chain Monte Carlo algorithms. These stochastic algorithms have been recently introduced to solve non-linear measure-valued equations. We provide an original theoretical analysis based on semigroup techniques on distribution spaces and fluctuation theorems for self-interacting random fields. Additionally we also present a series of sharp mean error bounds in terms of the semigroup associated with the first order expansion of the limiting measure-valued process. We illustrate our results in the context of Feynman--Kac semigroups", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Multivariate and functional central limit theorems, random fields, martingale limit theorems, self-interacting Markov chains, Markov chain Monte Carlo methods, Feynman--Kac semigroups", } @Article{Penrose:2009:NAI, author = "Mathew Penrose", title = "Normal Approximation for Isolated Balls in an Urn Allocation Model", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "74:2155--74:2181", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-699", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/699", abstract = "Consider throwing $n$ balls at random into $m$ urns, each ball landing in urn $i$ with probability $ p(i)$. Let $S$ be the resulting number of singletons, i.e., urns containing just one ball. We give an error bound for the Kolmogorov distance from the distribution of $S$ to the normal, and estimates on its variance. These show that if $n$, $m$ and $ (p(i))$ vary in such a way that $ n p(i)$ remains bounded uniformly in $n$ and $i$, then $S$ satisfies a CLT if and only if ($n$ squared) times the sum of the squares of the entries $ p(i)$ tends to infinity, and demonstrate an optimal rate of convergence in the CLT in this case. In the uniform case with all $ p(i)$ equal and with $m$ and $n$ growing proportionately, we provide bounds with better asymptotic constants. The proof of the error bounds is based on Stein's method via size-biased couplings.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "{Berry--Ess{\'e}en} bound, central limit theorem, occupancy scheme, size biased coupling, Stein's method", } @Article{Burdzy:2009:DSF, author = "Krzysztof Burdzy", title = "Differentiability of Stochastic Flow of Reflected {Brownian} Motions", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "75:2182--75:2240", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-700", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/700", abstract = "We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear map represented by a multiplicative functional for reflected Brownian motion. The method of proof is based on excursion theory and analysis of the deterministic Skorokhod equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Reflected Brownian motion, multiplicative functional", } @Article{Abreu:2009:TLP, author = "Victor Perez Abreu and Constantin Tudor", title = "On the Traces of {Laguerre} Processes", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "76:2241--76:2263", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-702", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/702", abstract = "Almost sure and $ L^k$-convergence of the traces of Laguerre processes to the family of dilations of the standard free Poisson distribution are established. We also prove that the fluctuations around the limiting process, converge weakly to a continuous centered Gaussian process. The almost sure convergence on compact time intervals of the largest and smallest eigenvalues processes is also established", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Matrix valued process, Complex Wishart distribution, Trace processes, Largest and smallest eigenvalues, Propagation of chaos, Fluctuations of moments, Free Poisson distribution", } @Article{Zhang:2009:TCV, author = "Yu Zhang", title = "The Time Constant Vanishes Only on the Percolation Cone in Directed First Passage Percolation", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "77:2264--77:2286", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-706", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/706", abstract = "We consider the directed first passage percolation model on $ \mathbb {Z}^2 $. In this model, we assign independently to each edge $e$ a passage time $ t(e)$ with a common distribution $F$. We denote by $ \vec {T}(0, (r, \theta))$ the passage time from the origin to $ (r, \theta)$ by a northeast path for $ (r, \theta) \in \mathbb {R}_+ \times [0, \pi / 2]$. It is known that $ \vec {T}(0, (r, \theta)) / r$ converges to a time constant $ \vec {\mu }_F(\theta)$. Let $ \vec {p}_c$ denote the critical probability for oriented percolation. In this paper, we show that the time constant has a phase transition at $ \vec {p}_c$, as follows: (1) If $ F(0) < \vec {p}_c$, then $ \vec {\mu }_F(\theta) > 0$ for all $ 0 \leq \theta \leq \pi / 2$. (2) If $ F(0) = \vec {p}_c$, then $ \vec {\mu }_F(\theta) > 0$ if and only if $ \theta \neq \pi / 4$. (3) If $ F(0) = p > \vec {p}_c$, then there exists a percolation cone between $ \theta_p^-$ and $ \theta_p^+$ for $ 0 \leq \theta^-_p < \theta^+_p \leq \pi / 2$ such that $ \vec {\mu }(\theta) > 0$ if and only if $ \theta \not \in [\theta_p^-, \theta^+_p]$. Furthermore, all the moments of $ \vec {T}(0, (r, \theta))$ converge whenever $ \theta \in [\theta_p^-, \theta^+_p]$. As applications, we describe the shape of the directed growth model on the distribution of $F$. We give a phase transition for the shape at $ \vec {p}_c$", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "directed first passage percolation, growth model, and phase transition", } @Article{Nourdin:2009:DFC, author = "Ivan Nourdin and Frederi Viens", title = "Density Formula and Concentration Inequalities with {Malliavin} Calculus", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "78:2287--78:2309", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-707", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/707", abstract = "We show how to use the Malliavin calculus to obtain a new exact formula for the density $ \rho $ of the law of any random variable $Z$ which is measurable and differentiable with respect to a given isonormal Gaussian process. The main advantage of this formula is that it does not refer to the divergence operator $ \delta $ (dual of the Malliavin derivative $D$). The formula is based on an auxiliary random variable $ G := < D Z, - D L^{-1}Z >_H$, where $L$ is the generator of the so-called Ornstein--Uhlenbeck semigroup. The use of $G$ was first discovered by Nourdin and Peccati (PTRF 145 75-118 2009 \url{http://www.ams.org/mathscinet-getitem?mr=2520122}MR-2520122), in the context of rates of convergence in law. Here, thanks to $G$, density lower bounds can be obtained in some instances. Among several examples, we provide an application to the (centered) maximum of a general Gaussian process. We also explain how to derive concentration inequalities for $Z$ in our framework.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "concentration inequality; density; fractional Brownian motion; Malliavin calculus; suprema of Gaussian processes", } @Article{Sakagawa:2009:CTD, author = "Hironobu Sakagawa", title = "Confinement of the Two Dimensional Discrete {Gaussian} Free Field Between Two Hard Walls", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "79:2310--79:2327", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-711", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/711", abstract = "We consider the two dimensional discrete Gaussian free field confined between two hard walls. We show that the field becomes massive and identify the precise asymptotic behavior of the mass and the variance of the field as the height of the wall goes to infinity. By large fluctuation of the field, asymptotic behaviors of these quantities in the two dimensional case differ greatly from those of the higher dimensional case studied by [S07].", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian field; hard wall; mass; random interface; random walk representation", } @Article{vanBargen:2009:AGS, author = "Holger van Bargen", title = "Asymptotic Growth of Spatial Derivatives of Isotropic Flows", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "80:2328--80:2351", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-704", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/704", abstract = "It is known from the multiplicative ergodic theorem that the norm of the derivative of certain stochastic flows at a previously fixed point grows exponentially fast in time as the flows evolves. We prove that this is also true if one takes the supremum over a bounded set of initial points. We give an explicit bound for the exponential growth rate which is far different from the lower bound coming from the Multiplicative Ergodic Theorem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic flows, isotropic Brownian flows, isotropic Ornstein--Uhlenbeck flows, asymptotic behavior of derivatives", } @Article{Barbour:2009:FCC, author = "Andrew Barbour and Svante Janson", title = "A Functional Combinatorial {Central Limit Theorem}", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "81:2352--81:2370", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-709", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/709", abstract = "The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the original random process. Distance is measured by comparison of expectations of smooth functionals of the processes, and the argument is by way of Stein's method. The pre-limiting process is then shown, under weak conditions, to converge to a Gaussian limit process. The theorem is used to describe the shape of random permutation tableaux.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "combinatorial central limit theorem; Gaussian process; permutation tableau; Stein's method", } @Article{Csaki:2009:SLT, author = "Endre Cs{\'a}ki and Mikl{\'o}s Cs{\"o}rg{\"o} and Antonia Feldes and P{\'a}l R{\'e}v{\'e}sz", title = "Strong Limit Theorems for a Simple Random Walk on the $2$-Dimensional Comb", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "82:2371--82:2390", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-710", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/710", abstract = "We study the path behaviour of a simple random walk on the $2$-dimensional comb lattice $ C^2$ that is obtained from $ \mathbb {Z}^2$ by removing all horizontal edges off the $x$-axis. In particular, we prove a strong approximation result for such a random walk which, in turn, enables us to establish strong limit theorems, like the joint Strassen type law of the iterated logarithm of its two components, as well as their marginal Hirsch type behaviour.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "2-dimensional comb; 2-dimensional Wiener process; iterated Brownian motion; Laws of the iterated logarithm; Random walk; strong approximation", } @Article{Bai:2009:CLS, author = "Zhidong Bai and Xiaoying Wang and Wang Zhou", title = "{CLT} for Linear Spectral Statistics of {Wigner} matrices", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "83:2391--83:2417", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-705", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/705", abstract = "In this paper, we prove that the spectral empirical process of Wigner matrices under sixth-moment conditions, which is indexed by a set of functions with continuous fourth-order derivatives on an open interval including the support of the semicircle law, converges weakly in finite dimensions to a Gaussian process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bernstein polynomial; central limit theorem; Stieltjes transform; Wigner matrices", } @Article{Birkner:2009:GSF, author = "Matthias Birkner and Jochen Blath", title = "Generalised Stable {Fleming--Viot} Processes as Flickering Random Measures", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "84:2418--84:2437", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-712", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/712", abstract = "We study some remarkable path-properties of generalised stable Fleming--Viot processes (including the so-called spatial Neveu superprocess), inspired by the notion of a ``wandering random measure'' due to Dawson and Hochberg (1982). In particular, we make use of Donnelly and Kurtz' (1999) modified lookdown construction to analyse their longterm scaling properties, exhibiting a rare natural example of a scaling family of probability laws converging in f.d.d. sense, but not weakly w.r.t. any of Skorohod's topologies on path space. This phenomenon can be explicitly described and intuitively understood in terms of ``sparks'', leading to the concept of a ``flickering random measure''. In particular, this completes results of Fleischmann and Wachtel (2006) about the spatial Neveu process and complements results of Dawson and Hochberg (1982) about the classical Fleming Viot process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Generalised Fleming--Viot process, flickering random measure, measure-valued diffusion, lookdown construction, wandering random measure, Neveu superprocess, path properties, tightness, Skorohod topology", } @Article{Dereudre:2009:VCG, author = "David Dereudre and Hans-Otto Georgii", title = "Variational Characterisation of {Gibbs} Measures with {Delaunay} Triangle Interaction", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "85:2438--85:2462", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-713", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/713", abstract = "This paper deals with stationary Gibbsian point processes on the plane with an interaction that depends on the tiles of the Delaunay triangulation of points via a bounded triangle potential. It is shown that the class of these Gibbs processes includes all minimisers of the associated free energy density and is therefore nonempty. Conversely, each such Gibbs process minimises the free energy density, provided the potential satisfies a weak long-range assumption.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Delaunay triangulation; free energy; Gibbs measure; large deviations; pressure; variational principle; Voronoi tessellation", } @Article{Bose:2009:LSD, author = "Arup Bose and Rajat Hazra and Koushik Saha", title = "Limiting Spectral Distribution of Circulant Type Matrices with Dependent Inputs", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "86:2463--86:2491", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-714", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/714", abstract = "Limiting spectral distribution (LSD) of scaled eigenvalues of circulant, symmetric circulant and a class of k-circulant matrices are known when the input sequence is independent and identically distributed with finite moments of suitable order. We derive the LSD of these matrices when the input sequence is a stationary, two sided moving average process of infinite order. The limits are suitable mixtures of normal, symmetric square root of the chi square, and other mixture distributions, with the spectral density of the process involved in the mixtures.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$k$ circulant matrix; circulant matrix; eigenvalues; empirical spectral distribution; Large dimensional random matrix; limiting spectral distribution; moving average process; normal; reverse circulant matrix; spectral density; symmetric circulant matrix", } @Article{Bercu:2009:AAB, author = "Bernard Bercu and Beno{\^\i}te de Saporta and Anne G{\'e}gout-Petit", title = "Asymptotic Analysis for Bifurcating Autoregressive Processes via a Martingale Approach", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "87:2492--87:2526", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-717", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/717", abstract = "We study the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "almost sure convergence; bifurcating autoregressive process; central limit theorem; least squares estimation; martingales; quadratic strong law; tree-indexed times series", } @Article{Blomker:2009:AES, author = "Dirk Bl{\"o}mker and Wael Mohammed", title = "Amplitude Equation for {SPDEs} with Quadratic Non-Linearities", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "88:2527--88:2550", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-716", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/716", abstract = "In this paper we rigorously derive stochastic amplitude equations for a rather general class of SPDEs with quadratic nonlinearities forced by small additive noise. Near a change of stability we use the natural separation of time-scales to show that the solution of the original SPDE is approximated by the solution of an amplitude equation, which describes the evolution of o dominant modes. Our results significantly improve older results. We focus on equations with quadratic nonlinearities and give applications to the one-dimensional Burgers? equation and a model from surface growth.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Amplitude equations, quadratic nonlinearities, separation of time-scales, SPDE", } @Article{Bessaih:2009:LDP, author = "Hakima Bessaih and Annie Millet", title = "Large Deviation Principle and Inviscid Shell Models", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "89:2551--89:2579", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-719", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/719", abstract = "LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient converges to 0 and the noise intensity is multiplied by its square root, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a $H$-valued Brownian motion satisfy a LDP in $ \mathcal {C}([0, T], V)$ for the topology of uniform convergence on $ [0, T]$, but where $V$ is endowed with a topology weaker than the natural one. The initial condition has to belong to $V$ and the proof is based on the weak convergence of a family of stochastic control equations. The rate function is described in terms of the solution to the inviscid equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "large deviations; Shell models of turbulence; stochastic PDEs; viscosity coefficient and inviscid models", } @Article{Caputo:2009:RTL, author = "Pietro Caputo and Alessandra Faggionato and Alexandre Gaudilliere", title = "Recurrence and Transience for Long-Range Reversible Random Walks on a Random Point Process", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "90:2580--90:2616", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-721", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/721", abstract = "We consider reversible random walks in random environment obtained from symmetric long-range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and the jump rate function. For recurrent models we obtain almost sure estimates on effective resistances in finite boxes. For transient models we construct explicit fluxes with finite energy on the associated electrical network.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walk in random environment, recurrence, transience, point process, electrical network", } @Article{Biau:2009:AND, author = "G{\'e}rard Biau and Benoit Cadre and David Mason and Bruno Pelletier", title = "Asymptotic Normality in Density Support Estimation", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "91:2617--91:2635", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-722", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/722", abstract = "Let $ X_1, \ldots, X_n $ be $n$ independent observations drawn from a multivariate probability density $f$ with compact support $ S_f$. This paper is devoted to the study of the estimator $ \hat {S}_n$ of $ S_f$ defined as the union of balls centered at the $ X_i$ and with common radius $ r_n$. Using tools from Riemannian geometry, and under mild assumptions on $f$ and the sequence $ (r_n)$, we prove a central limit theorem for $ \lambda (S_n \Delta S_f)$, where $ \lambda $ denotes the Lebesgue measure on $ \mathbb {R}^d$ and $ \Delta $ the symmetric difference operation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central limit theorem; Nonparametric statistics; Support estimation; Tubular neighborhood", } @Article{Doring:2009:MDR, author = "Hanna D{\"o}ring and Peter Eichelsbacher", title = "Moderate Deviations in a Random Graph and for the Spectrum of {Bernoulli} Random Matrices", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "92:2636--92:2656", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-723", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/723", abstract = "We prove the moderate deviation principle for subgraph count statistics of Erd{\H{o}}s--R{\'e}nyi random graphs. This is equivalent in showing the moderate deviation principle for the trace of a power of a Bernoulli random matrix. It is done via an estimation of the log-Laplace transform and the G{\"a}rtner-Ellis theorem. We obtain upper bounds on the upper tail probabilities of the number of occurrences of small subgraphs. The method of proof is used to show supplemental moderate deviation principles for a class of symmetric statistics, including non-degenerate U-statistics with independent or Markovian entries.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "concentration inequalities; Markov chains; moderate deviations; random graphs; random matrices; U-statistics", } @Article{DeBlassie:2009:EPB, author = "Dante DeBlassie", title = "The Exit Place of {Brownian} Motion in an Unbounded Domain", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "93:2657--93:2690", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-726", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/726", abstract = "For Brownian motion in an unbounded domain we study the influence of the ``far away'' behavior of the domain on the probability that the modulus of the Brownian motion is large when it exits the domain. Roughly speaking, if the domain expands at a sublinear rate, then the chance of a large exit place decays in a subexponential fashion. The decay rate can be explicitly given in terms of the sublinear expansion rate. Our results encompass and extend some known special cases.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Exit place of Brownian motion, parabolic-type domain, horn-shaped domain, $h$-transform, Green function, harmonic measure", } @Article{Linde:2009:SRF, author = "Werner Linde and Antoine Ayache", title = "Series Representations of Fractional {Gaussian} Processes by Trigonometric and {Haar} Systems", journal = j-ELECTRON-J-PROBAB, volume = "14", pages = "94:2691--94:2719", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v14-727", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/727", abstract = "The aim of the present paper is to investigate series representations of the Riemann--Liouville process $ R^\alpha $, $ \alpha > 1 / 2 $, generated by classical orthonormal bases in $ L_2 [0, 1] $. Those bases are, for example, the trigonometric or the Haar system. We prove that the representation of $ R^\alpha $ via the trigonometric system possesses the optimal convergence rate if and only if $ 1 / 2 < \alpha \leq 2 $. For the Haar system we have an optimal approximation rate if $ 1 / 2 < \alpha < 3 / 2 $ while for $ \alpha > 3 / 2 $ a representation via the Haar system is not optimal. Estimates for the rate of convergence of the Haar series are given in the cases $ \alpha > 3 / 2 $ and $ \alpha = 3 / 2 $. However, in this latter case the question whether or not the series representation is optimal remains open. Recently M. A. Lifshits answered this question (cf. [13]). Using a different approach he could show that in the case $ \alpha = 3 / 2 $ a representation of the Riemann--Liouville process via the Haar system is also not optimal.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Approximation of operators and processes, Rie-mann--Liouville operator, Riemann--Liouville process, Haar system, trigonometric system", } @Article{Bahadoran:2010:SHL, author = "Christophe Bahadoran and Herv{\'e} Guiol and Krishnamurthi Ravishankar and Ellen Saada", title = "Strong Hydrodynamic Limit for Attractive Particle Systems on $ \mathbb {Z} $", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "1:1--1:43", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-728", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/728", abstract = "We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on $ \mathbb {Z} $ starting from an arbitrary initial profile. We generalize earlier works by Seppalainen (1999) and Andjel et al. (2004). Our constructive approach requires new ideas since the subadditive ergodic theorem (central to previous works) is no longer effective in our setting.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "attractive particle system; entropy solution; Glimm scheme; graphical construction; non-convex or non-concave flux; non-explicit invariant measures; Strong (a.s.) hydrodynamics", } @Article{Watanabe:2010:RTI, author = "Toshiro Watanabe and Kouji Yamamuro", title = "Ratio of the Tail of an Infinitely Divisible Distribution on the Line to that of its {L{\'e}vy} Measure", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "2:44--2:74", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-732", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/732", abstract = "A necessary and sufficient condition for the tail of an infinitely divisible distribution on the real line to be estimated by the tail of its L{\'e}vy measure is found. The lower limit and the upper limit of the ratio of the right tail of an infinitely divisible distribution to the right tail of its L{\'e}vy measure are estimated from above and below by reviving Teugels's classical method. The exponential class and the dominated varying class are studied in detail.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "infinite divisibility, L'evy measure, $ O$-subexponentiality, dominated variation, exponential class", } @Article{Nordenstam:2010:SAD, author = "Eric Nordenstam", title = "On the Shuffling Algorithm for Domino Tilings", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "3:75--3:95", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-730", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/730", abstract = "We study the dynamics of a certain discrete model of interacting interlaced particles that comes from the so called shuffling algorithm for sampling a random tiling of an Aztec diamond. It turns out that the transition probabilities have a particularly convenient determinantal form. An analogous formula in a continuous setting has recently been obtained by Jon Warren studying certain model of interlacing Brownian motions which can be used to construct Dyson's non-intersecting Brownian motion. We conjecture that Warren's model can be recovered as a scaling limit of our discrete model and prove some partial results in this direction. As an application to one of these results we use it to rederive the known result that random tilings of an Aztec diamond, suitably rescaled near a turning point, converge to the GUE minor process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; random matrices; random tilings", } @Article{Fill:2010:PSV, author = "James Fill and Mark Huber", title = "Perfect Simulation of {Vervaat} Perpetuities", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "4:96--4:109", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-734", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/734", abstract = "We use coupling into and from the past to sample perfectly in a simple and provably fast fashion from the Vervaat family of perpetuities. The family includes the Dickman distribution, which arises both in number theory and in the analysis of the Quickselect algorithm (the motivation for our work).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coupling into and from the past; Dickman distribution; dominating chain; Markov chain; multigamma coupler; Perfect simulation; perpetuity; Quickselect; Vervaat perpetuities", } @Article{Li:2010:ELM, author = "Wenbo Li and Xinyi Zhang", title = "Expected Lengths of Minimum Spanning Trees for Non-identical Edge Distributions", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "5:110--5:141", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-735", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/735", abstract = "An exact general formula for the expected length of the minimal spanning tree (MST) of a connected (possibly with loops and multiple edges) graph whose edges are assigned lengths according to independent (not necessarily identical) distributed random variables is developed in terms of the multivariate Tutte polynomial (alias Potts model). Our work was inspired by Steele's formula based on two-variable Tutte polynomial under the model of uniformly identically distributed edge lengths. Applications to wheel graphs and cylinder graphs are given under two types of edge distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cylinder Graph; Expected Length; Minimum Spanning Tree; Random Graph; The Multivariate Tutte Polynomial; The Tutte Polynomial; Wheel Graph", } @Article{Fradon:2010:BDG, author = "Myriam Fradon", title = "{Brownian} Dynamics of Globules", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "6:142--6:161", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-739", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/739", abstract = "We prove the existence and uniqueness of a strong solution of a stochastic differential equation with normal reflection representing the random motion of finitely many globules. Each globule is a sphere with time-dependent random radius and a center moving according to a diffusion process. The spheres are hard, hence non-intersecting, which induces in the equation a reflection term with a local (collision-)time. A smooth interaction is considered too and, in the particular case of a gradient system, the reversible measure of the dynamics is given. In the proofs, we analyze geometrical properties of the boundary of the set in which the process takes its values, in particular the so-called Uniform Exterior Sphere and Uniform Normal Cone properties. These techniques extend to other hard core models of objects with a time-dependent random characteristic: we present here an application to the random motion of a chain-like molecule.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian globule; hard core interaction; local time; normal reflection; reversible measure; Stochastic Differential Equation", } @Article{Barton:2010:NME, author = "Nick Barton and Alison Etheridge and Amandine V{\'e}ber", title = "A New Model for Evolution in a Spatial Continuum", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "7:162--7:216", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-741", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/741", abstract = "We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming--Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans (1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of side length L as L tends to infinity. Under appropriate conditions (and on a suitable timescale) we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "genealogy, evolution, multiple merger coalescent, spatial continuum, spatial Lambda-coalescent, generalised Fleming--Viot process", } @Article{Limic:2010:SCI, author = "Vlada Limic", title = "On the Speed of Coming Down from Infinity for {$ \Xi $}-Coalescent Processes", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "8:217--8:240", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-742", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/742", abstract = "The $ \Xi $-coalescent processes were initially studied by M{\"o}hle and Sagitov (2001), and introduced by Schweinsberg (2000) in their full generality. They arise in the mathematical population genetics as the complete class of scaling limits for genealogies of Cannings' models. The $ \Xi $-coalescents generalize $ \Lambda $-coalescents, where now simultaneous multiple collisions of blocks are possible. The standard version starts with infinitely many blocks at time $0$, and it is said to come down from infinity if its number of blocks becomes immediately finite, almost surely. This work builds on the technique introduced recently by Berstycki, Berestycki and Limic (2009), and exhibits deterministic ``speed'' function - an almost sure small time asymptotic to the number of blocks process, for a large class of $ \Xi $-coalescents that come down from infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coming down from infinity; Exchangeable coalescents; martingale technique; small-time asymptotics", } @Article{Rhodes:2010:MMR, author = "R{\'e}mi Rhodes and Vincent Vargas", title = "Multidimensional Multifractal Random Measures", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "9:241--9:258", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-746", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/746", abstract = "We construct and study space homogeneous and isotropic random measures (MMRM) which generalize the so-called MRM measures constructed by previous authors. Our measures satisfy an exact scale invariance equation and are therefore natural models in dimension 3 for the dissipation measure in a turbulent flow.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random measures, Multifractal processes", } @Article{Faggionato:2010:HLZ, author = "Alessandra Faggionato", title = "Hydrodynamic Limit of Zero Range Processes Among Random Conductances on the Supercritical Percolation Cluster", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "10:259--10:291", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-748", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/748", abstract = "We consider i.i.d. random variables $ \omega = \{ \omega (b) \} $ parameterized by the family of bonds in $ \mathbb {Z}^d $, $ d > 1 $. The random variable $ \omega (b) $ is thought of as the conductance of bond $b$ and it ranges in a finite interval $ [0, c_0]$. Assuming the probability of the event $ \{ \omega (b) > 0 \} $ to be supercritical and denoting by $ C(\omega)$ the unique infinite cluster associated to the bonds with positive conductance, we study the zero range process on $ C(\omega)$ with $ \omega (b)$-proportional probability rate of jumps along bond $b$. For almost all realizations of the environment we prove that the hydrodynamic behavior of the zero range process is governed by a nonlinear heat equation, independent from $ \omega $. As byproduct of the above result and the blocking effect of the finite clusters, we discuss the bulk behavior of the zero range process on $ \mathbb {Z}^d$ with conductance field $ \omega $. We do not require any ellipticity condition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bond percolation; disordered system; homogenization; hydrodynamic limit; stochastic domination; zero range process", } @Article{Denisov:2010:CLT, author = "Denis Denisov and Vitali Wachtel", title = "Conditional Limit Theorems for Ordered Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "11:292--11:322", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-752", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/752", abstract = "In a recent paper of Eichelsbacher and Koenig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a $k$-dimensional random walk conditioned to stay in a strict order at all times. Moreover, they have shown that the rescaled random walk converges to the Dyson Brownian motion. In the present paper we find the optimal moment assumptions for the construction proposed by Eichelsbacher and Koenig, and generalise the limit theorem for this conditional process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dyson's Brownian Motion, Doob h-transform, Weyl chamber", } @Article{Barret:2010:UEM, author = "Florent Barret and Anton Bovier and Sylvie M{\'e}l{\'e}ard", title = "Uniform Estimates for Metastable Transition Times in a Coupled Bistable System", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "12:323--12:345", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-751", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/751", abstract = "We consider a coupled bistable $N$-particle system on $ \mathbb {R}^N$ driven by a Brownian noise, with a strong coupling corresponding to the synchronised regime. Our aim is to obtain sharp estimates on the metastable transition times between the two stable states, both for fixed $N$ and in the limit when $N$ tends to infinity, with error estimates uniform in $N$. These estimates are a main step towards a rigorous understanding of the metastable behavior of infinite dimensional systems, such as the stochastically perturbed Ginzburg--Landau equation. Our results are based on the potential theoretic approach to metastability.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "capacity estimates; coupled bistable systems; Metastability; metastable transition time; stochastic Ginzburg--Landau equation", } @Article{Cattiaux:2010:FIH, author = "Patrick Cattiaux and Nathael Gozlan and Arnaud Guillin and Cyril Roberto", title = "Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "13:346--13:385", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-754", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/754", abstract = "This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as weak Poincar{\'e} and weak Cheeger, weighted Poincar{\'e} and weighted Cheeger inequalities and their dual forms. Proofs are short and we cover very large situations. For product measures on $ \mathbb {R}^n $ we obtain the optimal dimension dependence using the mass transportation method. Then we derive (optimal) isoperimetric inequalities. Finally we deal with spherically symmetric measures. We recover and improve many previous result", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "weighted Poincar{\'e} inequalities, weighted Cheeger inequalities, Lyapunov function, weak inequalities, isoperimetric profile", } @Article{Andjel:2010:SSM, author = "Enrique Andjel and Judith Miller and Etienne Pardoux", title = "Survival of a Single Mutant in One Dimension", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "14:386--14:408", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-769", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/769", abstract = "We study a one dimensional two-type contact process with equal rate of propagation (and death) of the two types. We show that the progeny of a finite number of mutants has a positive probability of survival if and only at time 0 there is at most a finite number of residents on at least one side of the mutant's ``colony''.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "two-type contact process, survival", } @Article{Kinnally:2010:EUS, author = "Michael Kinnally and Ruth Williams", title = "On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Positivity Constraints", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "15:409--15:451", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-756", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/756", abstract = "Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. There is interest in understanding what effect noise has on the behavior of such models. Here we consider a multidimensional stochastic delay differential equation with normal reflection as a noisy analogue of a deterministic system with delayed feedback and positivity constraints. We obtain sufficient conditions for existence and uniqueness of stationary distributions for such equations. The results are applied to an example from Internet rate control and a simple biochemical reaction system.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic differential equation, delay equation, stationary distribution, normal reflection, Lyapunov/Razumikhin-type argument, asymptotic coupling", } @Article{Feng:2010:LTR, author = "Chunrong Feng and Huaizhong Zhao", title = "Local Time Rough Path for {L{\'e}vy} Processes", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "16:452--16:483", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-770", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/770", abstract = "In this paper, we will prove that the local time of a L{\'e}vy process is a rough path of roughness $p$ a.s. for any $ 2 < p < 3$ under some condition for the L{\'e}vy measure. This is a new class of rough path processes. Then for any function $g$ of finite $q$-variation ($ 1 \leq q < 3$), we establish the integral $ \int_{- \infty }^{\infty }g(x)d L_t^x$ as a Young integral when $ 1 \leq q < 2$ and a Lyons' rough path integral when $ 2 \leq q < 3$. We therefore apply these path integrals to extend the Tanaka--Meyer formula for a continuous function $f$ if $ f^\prime_-$ exists and is of finite $q$-variation when $ 1 \leq q < 3$, for both continuous semi-martingales and a class of L{\'e}vy processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "geometric rough path; L'evy processes; rough path integral; semimartingale local time; Young integral", } @Article{Bo:2010:STS, author = "Lijun Bo and Kehua Shi and Yongjin Wang", title = "Support Theorem for a Stochastic {Cahn--Hilliard} Equation", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "17:484--17:525", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-760", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/760", abstract = "In this paper, we establish a Stroock--Varadhan support theorem for the global mild solution to a $d$ ($ d \leq 3$)-dimensional stochastic Cahn--Hilliard partial differential equation driven by a space-time white noise", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Space-time white noise; Stochastic Cahn--Hilliard equation; Stroock--Varadhan support theorem", } @Article{Erdos:2010:USK, author = "Laszlo Erdos and Jose Ramirez and Benjamin Schlein and Horng-Tzer Yau", title = "Universality of Sine-Kernel for {Wigner} Matrices with a Small {Gaussian} Perturbation", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "18:526--18:604", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-768", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/768", abstract = "We consider $ N \times N $ Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance $ N^{-3 / 4 + \beta } $ for some positive $ \beta > 0 $. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Wigner random matrix, Dyson sine kernel", } @Article{Jacquot:2010:HLL, author = "Stephanie Jacquot", title = "A Historical Law of Large Numbers for the {Marcus--Lushnikov} Process", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "19:605--19:635", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-767", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/767", abstract = "The Marcus--Lushnikov process is a finite stochastic particle system, in which each particle is entirely characterized by its mass. Each pair of particles with masses $x$ and $y$ merges into a single particle at a given rate $ K(x, y)$. Under certain assumptions, this process converges to the solution to the Smoluchowski coagulation equation, as the number of particles increases to infinity. The Marcus--Lushnikov process gives at each time the distribution of masses of the particles present in the system, but does not retain the history of formation of the particles. In this paper, we set up a historical analogue of the Marcus--Lushnikov process (built according to the rules of construction of the usual Markov-Lushnikov process) each time giving what we call the historical tree of a particle. The historical tree of a particle present in the Marcus--Lushnikov process at a given time t encodes information about the times and masses of the coagulation events that have formed that particle. We prove a law of large numbers for the empirical distribution of such historical trees. The limit is a natural measure on trees which is constructed from a solution to the Smoluchowski coagulation equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coupling; historical trees; limit measure on trees; Marcus--Lushnikov process on trees; Smoluchowski coagulation equation; tightness", } @Article{Nagahata:2010:LCL, author = "Yukio Nagahata and Nobuo Yoshida", title = "Localization for a Class of Linear Systems", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "20:636--20:653", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-757", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/757", abstract = "We consider a class of continuous-time stochastic growth models on d-dimensional lattice with non-negative real numbers as possible values per site. The class contains examples such as binary contact path process and potlatch process. We show the equivalence between the slow population growth and localization property that the time integral of the replica overlap diverges. We also prove, under reasonable assumptions, a localization property in a stronger form that the spatial distribution of the population does not decay uniformly in space.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "binary contact path process; linear systems; localization; potlatch process", } @Article{Berger:2010:CPR, author = "Quentin Berger and Fabio Toninelli", title = "On the Critical Point of the Random Walk Pinning Model in Dimension d=3", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "21:654--21:683", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-761", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/761", abstract = "We consider the Random Walk Pinning Model studied in [Birkner--Sun 2008] and [Birkner--Greven--den Hollander 2008]: this is a random walk $X$ on $ \mathbb {Z}^d$, whose law is modified by the exponential of beta times the collision local time up to time $N$ with the (quenched) trajectory $Y$ of another $d$-dimensional random walk. If $ \beta $ exceeds a certain critical value $ \beta_c$, the two walks stick together for typical $Y$ realizations (localized phase). A natural question is whether the disorder is relevant or not, that is whether the quenched and annealed systems have the same critical behavior. Birkner and Sun proved that $ \beta_c$ coincides with the critical point of the annealed Random Walk Pinning Model if the space dimension is $ d = 1$ or $ d = 2$, and that it differs from it in dimension $d$ larger or equal to $4$ (for $d$ strictly larger than $4$, the result was proven also in [Birkner-Greven-den Hollander 2008]). Here, we consider the open case of the marginal dimension $ d = 3$, and we prove non-coincidence of the critical points.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Pinning Models, Random Walk, Fractional Moment Method, Marginal Disorder", } @Article{Beghin:2010:PTP, author = "Luisa Beghin and Enzo Orsingher", title = "{Poisson}-Type Processes Governed by Fractional and Higher-Order Recursive Differential Equations", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "22:684--22:709", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-762", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/762", abstract = "We consider some fractional extensions of the recursive differential equation governing the Poisson process, i.e., $ \partial_t p_k(t) = - \lambda (p_k(t) - p_{k - 1}(t)) $, $ k \geq 0 $, $ t > 0 $ by introducing fractional time-derivatives of order $ \nu, 2 \nu, \ldots, n \nu $. We show that the so-called ``Generalized Mittag-Leffler functions'' $ E_{\alpha, \beta^k}(x) $, $ x \in \mathbb {R} $ (introduced by Prabhakar [24] )arise as solutions of these equations. The corresponding processes are proved to be renewal, with density of the inter-arrival times (represented by Mittag-Leffler functions) possessing power, instead of exponential, decay, for $ t \to \infty $. On the other hand, near the origin the behavior of the law of the interarrival times drastically changes for the parameter $ \nu $ varying in $ (0, 1] $. For integer values of $ \nu $, these models can be viewed as a higher-order Poisson processes, connected with the standard case by simple and explict relationships.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cox process.; Fractional difference-differential equations; Fractional Poisson processes; Generalized Mittag-Leffler functions; Processes with random time; Renewal function", } @Article{Revelle:2010:CCR, author = "David Revelle and Russ Thompson", title = "Critical Constants for Recurrence on Groups of Polynomial Growth", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "23:710--23:722", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-773", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/773", abstract = "The critical constant for recurrence, $ c_{rt} $, is an invariant of the quotient space $ H / G $ of a finitely generated group. The constant is determined by the largest moment a probability measure on $G$ can have without the induced random walk on $ H / G$ being recurrent. We present a description of which subgroups of groups of polynomial volume growth are recurrent. Using this we show that for such recurrent subgroups $ c_{rt}$ corresponds to the relative growth rate of $H$ in $G$, and in particular $ c_{rt}$ is either $0$, $1$ or $2$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "nilpotent group; random walk; recurrence; Schreier graph; volume growth", } @Article{Shellef:2010:ISP, author = "Eric Shellef", title = "{IDLA} on the Supercritical Percolation Cluster", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "24:723--24:740", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-775", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/775", abstract = "We consider the internal diffusion limited aggregation (IDLA) process on the infinite cluster in supercritical Bernoulli bond percolation on $ \mathbb {Z}^d $. It is shown that the process on the cluster behaves like it does on the Euclidean lattice, in that the aggregate covers all the vertices in a Euclidean ball around the origin, such that the ratio of vertices in this ball to the total number of particles sent out approaches one almost surely.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Key words and phrases: Internal Diffusion Limited Aggregation, IDLA, Supercritical percolation", } @Article{Addario-Berry:2010:CRG, author = "Louigi Addario-Berry and Nicolas Broutin and Christina Goldschmidt", title = "Critical Random Graphs: Limiting Constructions and Distributional Properties", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "25:741--25:775", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-772", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/772", abstract = "We consider the Erd{\H{o}}s--R{\'e}nyi random graph $ G(n, p) $ inside the critical window, where $ p = 1 / n + \lambda n^{-4 / 3} $ for some $ \lambda \in \mathbb {R} $. We proved in [1] that considering the connected components of $ G(n, p) $ as a sequence of metric spaces with the graph distance rescaled by $ n^{-1 / 3} $ and letting $ n \to \infty $ yields a non-trivial sequence of limit metric spaces $ C = (C_1, C_2, \ldots) $. These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on $ \mathbb {R}_+ $. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of [29] by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian excursion; continuum random tree; Gromov--Hausdorff distance; Poisson process; random graph; real tree; scaling limit; urn model", } @Article{Delmas:2010:TOF, author = "Jean-Fran{\c{c}}ois Delmas and Jean-St{\'e}phane Dhersin and Arno Siri-Jegousse", title = "On the Two Oldest Families for the {Wright--Fisher} Process", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "26:776--26:800", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-771", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/771", abstract = "We extend some of the results of Pfaffelhuber and Wakolbinger on the process of the most recent common ancestors in evolving coalescent by taking into account the size of one of the two oldest families or the oldest family which contains the immortal line of descent. For example we give an explicit formula for the Laplace transform of the extinction time for the Wright--Fisher diffusion. We give also an interpretation of the quasi-stationary distribution of the Wright--Fisher diffusion using the process of the relative size of one of the two oldest families, which can be seen as a resurrected Wright--Fisher diffusion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Wright--Fisher diffusion, MRCA, Kingman coalescent tree, resurrected process, quasi-stationary distribution", } @Article{vanderHofstad:2010:CCF, author = "Remco van der Hofstad and Akira Sakai", title = "Convergence of the Critical Finite-Range Contact Process to Super-{Brownian} Motion Above the Upper Critical Dimension: The Higher-Point Functions", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "27:801--27:894", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-783", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/783", abstract = "In this paper, we investigate the contact process higher-point functions which denote the probability that the infection started at the origin at time 0 spreads to an arbitrary number of other individuals at various later times. Together with the results of the two-point function in [16], on which our proofs crucially rely, we prove that the higher-point functions converge to the moment measures of the canonical measure of super-Brownian motion above the upper critical dimension 4. We also prove partial results for in dimension at most 4 in a local mean-field setting. The proof is based on the lace expansion for the time-discretized contact process, which is a version of oriented percolation. For ordinary oriented percolation, we thus reprove the results of [20]. The lace expansion coefficients are shown to obey bounds uniformly in the discretization parameter, which allows us to establish the scaling results also for the contact process We also show that the main term of the vertex factor, which is one of the non-universal constants in the scaling limit, is 1 for oriented percolation, and 2 for the contact process, while the main terms of the other non-universal constants are independent of the discretization parameter. The lace expansion we develop in this paper is adapted to both the higher-point functions and the survival probability. This unified approach makes it easier to relate the expansion coefficients derived in this paper and the expansion coefficients for the survival probability, which will be investigated in a future paper [18].", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "contact process, mean-field behavior, critical exponents, super-Brownian motion", } @Article{Lachal:2010:JDP, author = "Aim{\'e} Lachal and Valentina Cammarota", title = "Joint Distribution of the Process and its Sojourn Time on the Positive Half-Line for Pseudo-Processes Governed by High-Order Heat Equation", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "28:895--28:931", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-782", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/782", abstract = "Consider the high-order heat-type equation $ \partial_t u = \pm \partial^n_x u $ for an integer $ n > 2 $ and introduce the related Markov pseudo-process $ (X(t))_{t \geq 0} $. In this paper, we study the sojourn time $ T(t) $ in the interval $ [0, + \infty) $ up to a fixed time $t$ for this pseudo-process. We provide explicit expressions for the joint distribution of the couple $ (T(t), X(t))$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "pseudo-process, joint distribution of the process and its sojourn time, Spitzer's identity", } @Article{Hirsch:2010:LMA, author = "Francis Hirsch and Marc Yor", title = "Looking for Martingales Associated to a Self-Decomposable Law", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "29:932--29:961", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-786", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/786", abstract = "We construct martingales whose 1-dimensional marginals are those of a centered self-decomposable variable multiplied by some power of time $t$. Many examples involving quadratic functionals of Bessel processes are discussed", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Convex order, Self-decomposable law, Sato process, Karhunen--Lo{\'e}ve representation, Perturbed Bessel process, Ray--Knight theorem", } @Article{Eichelsbacher:2010:SMD, author = "Peter Eichelsbacher and Matthias Loewe", title = "{Stein}'s Method for Dependent Random Variables Occurring in Statistical Mechanics", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "30:962--30:988", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-777", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/777", abstract = "We develop Stein's method for exchangeable pairs for a rich class of distributional approximations including the Gaussian distributions as well as the non-Gaussian limit distributions. As a consequence we obtain convergence rates in limit theorems of partial sums for certain sequences of dependent, identically distributed random variables which arise naturally in statistical mechanics, in particular in the context of the Curie--Weiss models. Our results include a {Berry--Ess{\'e}en} rate in the Central Limit Theorem for the total magnetization in the classical Curie--Weiss model, for high temperatures as well as at the critical temperature, where the Central Limit Theorem fails. Moreover, we analyze {Berry--Ess{\'e}en} bounds as the temperature converges to one and obtain a threshold for the speed of this convergence. Single spin distributions satisfying the Griffiths--Hurst--Sherman (GHS) inequality like models of liquid helium or continuous Curie--Weiss models are considered.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "{Berry--Ess{\'e}en} bound, Stein's method, exchangeable pairs, Curie Weiss models, critical temperature, GHS-inequality", } @Article{Rhodes:2010:SHR, author = "Remi Rhodes", title = "Stochastic Homogenization of Reflected Stochastic Differential Equations", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "31:989--31:1023", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-776", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/776", abstract = "We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective local time. We prove that the limiting process is a reflected non-standard Brownian motion. Beyond the result, this problem is known as a prototype of non-translation invariant problem making the usual method of the ``environment as seen from the particle'' inefficient.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "functional limit theorem; homogenization; local time; random medium; reflected stochastic differential equation; Skorohod problem", } @Article{Peterson:2010:SOD, author = "Jonathon Peterson", title = "Systems of One-Dimensional Random Walks in a Common Random Environment", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "32:1024--32:1040", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-784", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/784", abstract = "We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed. We give upper bounds on the quenched probability that at least one of the random walks started in an interval has experience a large deviation slowdown. This leads to both a uniform law of large numbers and a hydrodynamic limit for the system of random walks. We also identify a family of distributions on the configuration of particles (parameterized by particle density) which are stationary under the (quenched) dynamics of the random walks and show that these are the limiting distributions for the system when started from a certain natural collection of distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "hydrodynamic limit; large deviations; Random walk in random environment", } @Article{Ondrejat:2010:SNL, author = "Martin Ondrejat", title = "Stochastic Non-Linear Wave Equations in Local {Sobolev} Spaces", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "33:1041--33:1091", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-789", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/789", abstract = "Existence of weak solutions of stochastic wave equations with nonlinearities of a critical growth driven by spatially homogeneous Wiener processes is established in local Sobolev spaces and local energy estimates for these solutions are proved. A new method to construct weak solutions is employed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic wave equation", } @Article{Zeindler:2010:PMM, author = "Dirk Zeindler", title = "Permutation Matrices and the Moments of their Characteristics Polynomials", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "34:1092--34:1118", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-781", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/781", abstract = "In this paper, we are interested in the moments of the characteristic polynomial $ Z_n(x) $ of the $ n \times n $ permutation matrices with respect to the uniform measure. We use a combinatorial argument to write down the generating function of $ E[\prod_{k = 1}^p Z_n^{s_k}(x_k)] $ for $ s_k \in \mathbb {N} $. We show with this generating function that $ \lim_{n \to \infty }E[\prod_{k = 1}^p Z_n^{s_k}(x_k)] $ exists for $ \max_k|x_k| < 1 $ and calculate the growth rate for $ p = 2 $, $ |x_1 | = |x_2 | = 1 $, $ x_1 = x_2 $ and $ n \to \infty $. We also look at the case $ s_k \in \mathbb {C} $. We use the Feller coupling to show that for each $ |x| < 1 $ and $ s \in \mathbb {C} $ there exists a random variable $ Z_\infty^s(x) $ such that $ Z_n^s(x) \overset {d}{\to }Z_\infty^s(x) $ and $ E[\prod_{k = 1}^p Z_n^{s_k}(x_k)] \to E[\prod_{k = 1}^p Z_\infty^{s_k}(x_k)] $ for $ \max_k|x_k| < 1 $ and $ n \to \infty $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random permutation matrices, symmetric group, characteristic polynomials, Feller coupling, asymptotic behavior of moments, generating functions", } @Article{Aoyama:2010:NFM, author = "Takahiro Aoyama and Alexander Lindner and Makoto Maejima", title = "A New Family of Mappings of Infinitely Divisible Distributions Related to the {Goldie--Steutel--Bondesson} Class", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "35:1119--35:1142", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-791", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/791", abstract = "Let $ \{ X_t^\mu, t \geq 0 \} $ be a L{\'e}vy process on $ \mathbb {R}^d $ whose distribution at time $1$ is a $d$-dimensional infinitely distribution $ \mu $. It is known that the set of all infinitely divisible distributions on $ \mathbb {R}^d$, each of which is represented by the law of a stochastic integral $ \int_0^1 \! \log (1 / t) \, d X_t^\mu $ for some infinitely divisible distribution on $ \mathbb {R}^d$, coincides with the Goldie-Steutel-Bondesson class, which, in one dimension, is the smallest class that contains all mixtures of exponential distributions and is closed under convolution and weak convergence. The purpose of this paper is to study the class of infinitely divisible distributions which are represented as the law of $ \int_0^1 \! (\log (1 / t))^{1 / \alpha } \, d X_t^\mu $ for general $ \alpha > 0$. These stochastic integrals define a new family of mappings of infinitely divisible distributions. We first study properties of these mappings and their ranges. Then we characterize some subclasses of the range by stochastic integrals with respect to some compound Poisson processes. Finally, we investigate the limit of the ranges of the iterated mappings.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "compound Poisson process; infinitely divisible distribution; limit of the ranges of the iterated mappings; stochastic integral mapping; the Goldie-Steutel-Bondesson class", } @Article{Windisch:2010:ERW, author = "David Windisch", title = "Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "36:1143--36:1160", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-787", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/787", abstract = "We study the entropy of the distribution of the set $ R_n $ of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of $ R_n $ if the graph is uniformly transient, and sublinearly in the expected size if the graph is uniformly recurrent with subexponential volume growth. This in particular answers a question asked by Benjamini, Kozma, Yadin and Yehudayoff (preprint).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walk, range, entropy", } @Article{Uchiyama:2010:GFT, author = "Kohei Uchiyama", title = "The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "37:1161--37:1189", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-793", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/793", abstract = "We obtain asymptotic estimates of the Green functions of random walks on the two-dimensional integer lattice that are killed on the horizontal axis. A basic asymptotic formula whose leading term is virtually the same as the explicit formula for the corresponding Green function of Brownian motion is established under the existence of second moments only. Some refinement of it is given under a slightly stronger moment condition. The extension of the results to random walks on the higher dimensional lattice is also given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "asymptotic formula, Green function, random walk of zero mean and finite variances, absorption on a line", } @Article{Cox:2010:CTD, author = "J. Theodore Cox and Mathieu Merle and Edwin Perkins", title = "Coexistence in a Two-Dimensional {Lotka--Volterra} Model", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "38:1190--38:1266", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-795", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/795", abstract = "We study the stochastic spatial model for competing species introduced by Neuhauser and Pacala in two spatial dimensions. In particular we confirm a conjecture of theirs by showing that there is coexistence of types when the competition parameters between types are equal and less than, and close to, the within types parameter. In fact coexistence is established on a thorn-shaped region in parameter space including the above piece of the diagonal. The result is delicate since coexistence fails for the two-dimensional voter model which corresponds to the tip of the thorn. The proof uses a convergence theorem showing that a rescaled process converges to super-Brownian motion even when the parameters converge to those of the voter model at a very slow rate.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coalescing random walk; coexistence; Lotka--Volterra; spatial competition; super-Brownian motion; survival; voter model", } @Article{Bardina:2010:WCS, author = "Xavier Bardina and Maria Jolis and Llu{\'\i}s Quer-Sardanyons", title = "Weak Convergence for the Stochastic Heat Equation Driven by {Gaussian} White Noise", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "39:1267--39:1295", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-792", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/792", abstract = "In this paper, we consider a quasi-linear stochastic heat equation with spatial dimension one, with Dirichlet boundary conditions and controlled by the space-time white noise. We formally replace the random perturbation by a family of noisy inputs depending on a parameter that approximate the white noise in some sense. Then, we provide sufficient conditions ensuring that the real-valued mild solution of the SPDE perturbed by this family of noises converges in law, in the space of continuous functions, to the solution of the white noise driven SPDE. Making use of a suitable continuous functional of the stochastic convolution term, we show that it suffices to tackle the linear problem. For this, we prove that the corresponding family of laws is tight and we identify the limit law by showing the convergence of the finite dimensional distributions. We have also considered two particular families of noises to that our result applies. The first one involves a Poisson process in the plane and has been motivated by a one-dimensional result of Stroock. The second one is constructed in terms of the kernels associated to the extension of Donsker's theorem to the plane.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Donsker kernels; stochastic heat equation; two-parameter Poisson process; weak convergence; white noise", } @Article{Szablowski:2010:MNR, author = "Pawel Szablowski", title = "Multidimensional $q$-Normal and Related Distributions --- {Markov} Case", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "40:1296--40:1318", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-796", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/796", abstract = "We define and study distributions in $ \mathbb {R}^d $ that we call $q$-Normal. For $ q = 1$ they are really multidimensional Normal, for $q$ in $ ( - 1, 1)$ they have densities, compact support and many properties that resemble properties of ordinary multidimensional Normal distribution. We also consider some generalizations of these distributions and indicate close relationship of these distributions to Askey--Wilson weight function i.e., weight with respect to which Askey--Wilson polynomials are orthogonal and prove some properties of this weight function. In particular we prove a generalization of Poisson--Mehler expansion formula", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Normal distribution, Poisson--Mehler expansion formula, q-Hermite, Al-Salam-Chihara Chebyshev, Askey--Wilson polynomials, Markov property", } @Article{Ledoux:2010:SDB, author = "Michel Ledoux and Brian Rider", title = "Small Deviations for Beta Ensembles", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "41:1319--41:1343", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-798", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/798", abstract = "We establish various small deviation inequalities for the extremal (soft edge) eigenvalues in the beta-Hermite and beta-Laguerre ensembles. In both settings, upper bounds on the variance of the largest eigenvalue of the anticipated order follow immediately.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random matrices, eigenvalues, small deviations", } @Article{Barbour:2010:CPA, author = "A. D. Barbour and Oliver Johnson and Ioannis Kontoyiannis and Mokshay Madiman", title = "Compound {Poisson} Approximation via Information Functionals", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "42:1344--42:1369", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-799", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/799", abstract = "An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Nonasymptotic bounds are derived for the distance between the distribution of a sum of independent integer-valued random variables and an appropriately chosen compound Poisson law. In the case where all summands have the same conditional distribution given that they are non-zero, a bound on the relative entropy distance between their sum and the compound Poisson distribution is derived, based on the data-processing property of relative entropy and earlier Poisson approximation results. When the summands have arbitrary distributions, corresponding bounds are derived in terms of the total variation distance. The main technical ingredient is the introduction of two ``information functionals, '' and the analysis of their properties. These information functionals play a role analogous to that of the classical Fisher information in normal approximation. Detailed comparisons are made between the resulting inequalities and related bounds.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Compound Poisson approximation, Fisher information, information theory, relative entropy, Stein's method", } @Article{Schilling:2010:SAS, author = "Rene Schilling and Alexander Schnurr", title = "The Symbol Associated with the Solution of a Stochastic Differential Equation", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "43:1369--43:1393", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-807", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/807", abstract = "We consider stochastic differential equations which are driven by multidimensional Levy processes. We show that the infinitesimal generator of the solution is a pseudo-differential operator whose symbol is calculated explicitly. For a large class of Feller processes many properties of the sample paths can be derived by analysing the symbol. It turns out that the solution of the SDE under consideration is a Feller process if the coefficient of the SDE is bounded and that the symbol is of a particularly nice structure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Blumenthal-Getoor index; L'evy process; pseudo-differential operator; sample path properties; semimartingale; stochastic differential equation", } @Article{Broman:2010:UBC, author = "Erik Broman and Federico Camia", title = "Universal Behavior of Connectivity Properties in Fractal Percolation Models", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "44:1394--44:1414", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-805", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/805", abstract = "Partially motivated by the desire to better understand the connectivity phase transition in fractal percolation, we introduce and study a class of continuum fractal percolation models in dimension $ d \geq 2 $. These include a scale invariant version of the classical (Poisson) Boolean model of stochastic geometry and (for $ d = 2$) the Brownian loop soup introduced by Lawler and Werner. The models lead to random fractal sets whose connectivity properties depend on a parameter $ \lambda $. In this paper we mainly study the transition between a phase where the random fractal sets are totally disconnected and a phase where they contain connected components larger than one point. In particular, we show that there are connected components larger than one point at the unique value of $ \lambda $ that separates the two phases (called the critical point). We prove that such a behavior occurs also in Mandelbrot's fractal percolation in all dimensions $ d \geq 2$. Our results show that it is a generic feature, independent of the dimension or the precise definition of the model, and is essentially a consequence of scale invariance alone. Furthermore, for $ d = 2$ we prove that the presence of connected components larger than one point implies the presence of a unique, unbounded, connected component.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random fractals, fractal percolation, continuum percolation, Mandelbrot percolation, phase transition, crossing probability, discontinuity, Brownian loop soup, Poisson Boolean Model", } @Article{Grimmett:2010:PSE, author = "Geoffrey Grimmett and Alexander Holroyd", title = "Plaquettes, Spheres, and Entanglement", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "45:1415--45:1428", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-804", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/804", abstract = "The high-density plaquette percolation model in $d$ dimensions contains a surface that is homeomorphic to the $ (d - 1)$-sphere and encloses the origin. This is proved by a path-counting argument in a dual model. When $ d = 3$, this permits an improved lower bound on the critical point $ p_e$ of entanglement percolation, namely $ p_e \geq \mu^{-2}$ where $ \mu $ is the connective constant for self-avoiding walks on $ \mathbb {Z}^3$. Furthermore, when the edge density $p$ is below this bound, the radius of the entanglement cluster containing the origin has an exponentially decaying tail.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "entanglement; percolation; random sphere", } @Article{Abraham:2010:PLC, author = "Romain Abraham and Jean-Fran{\c{c}}ois Delmas and Guillaume Voisin", title = "Pruning a {L{\'e}vy} Continuum Random Tree", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "46:1429--46:1473", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-802", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/802", abstract = "Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated L{\'e}vy continuum random tree. This pruning procedure is defined by adding some marks on the tree, using L'evy snake techniques. We then prove that the resulting sub-tree after pruning is still a L'evy continuum random tree. This last result is proved using the exploration process that codes the CRT, a special Markov property and martingale problems for exploration processes. We finally give the joint law under the excursion measure of the lengths of the excursions of the initial exploration process and the pruned one.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "continuum random tree, L{\'e}vy snake, special Markov property", } @Article{Davies:2010:EMM, author = "E. Davies", title = "Embeddable {Markov} Matrices", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "47:1474--47:1486", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-733", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/733", abstract = "We give an account of some results, both old and new, about any $ n \times n $ Markov matrix that is embeddable in a one-parameter Markov semigroup. These include the fact that its eigenvalues must lie in a certain region in the unit ball. We prove that a well-known procedure for approximating a non-embeddable Markov matrix by an embeddable one is optimal in a certain sense.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "eigenvalues; embeddability; Markov generator; Markov matrix", } @Article{Giovanni:2010:MDG, author = "Peccati Giovanni and Cengbo Zheng", title = "Multi-Dimensional {Gaussian} Fluctuations on the {Poisson} Space", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "48:1487--48:1527", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-813", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/813", abstract = "We study multi-dimensional normal approximations on the Poisson space by means of Malliavin calculus, Stein's method and probabilistic interpolations. Our results yield new multi-dimensional central limit theorems for multiple integrals with respect to Poisson measures - thus significantly extending previous works by Peccati, Sol{\'e}, Taqqu and Utzet. Several explicit examples (including in particular vectors of linear and non-linear functionals of Ornstein--Uhlenbeck L{\'e}vy processes) are discussed in detail.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central Limit Theorems; Malliavin calculus; Multi-dimensional normal approximations; Ornstein--Uhlenbeck processes; Poisson measures; Probabilistic Interpolations; Stein's method", } @Article{Marinelli:2010:WPA, author = "Carlo Marinelli and Michael Roeckner", title = "Well Posedness and Asymptotic Behavior for Stochastic Reaction--Diffusion Equations with Multiplicative {Poisson} Noise", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "49:1529--49:1555", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-818", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/818", abstract = "We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of invariant measures for the associated semigroup in the Markovian case. A key role is played by a new maximal inequality for stochastic convolutions in $ L_p $ spaces.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic PDE, reaction-diffusion equations, Poisson measures, monotone operators", } @Article{Seidler:2010:EES, author = "Jan Seidler", title = "Exponential Estimates for Stochastic Convolutions in $2$-Smooth {Banach} Spaces", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "50:1556--50:1573", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-808", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/808", abstract = "Sharp constants in a (one-sided) Burkholder--Davis--Gundy type estimate for stochastic integrals in a 2-smooth Banach space are found. As a consequence, exponential tail estimates for stochastic convolutions are obtained via Zygmund's extrapolation theorem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Burkholder--Davis--Gundy inequality; exponential tail estimates; stochastic convolutions; stochastic integrals in 2-smooth Banach spaces", } @Article{Bandyopadhyay:2010:ODL, author = "Antar Bandyopadhyay and Rahul Roy and Anish Sarkar", title = "On the One Dimensional {``Learning from Neighbours''} Model", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "51:1574--51:1593", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-809", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/809", abstract = "We consider a model of a discrete time ``interacting particle system'' on the integer line where infinitely many changes are allowed at each instance of time. We describe the model using chameleons of two different colours, {\em viz.}, red (R) and blue (B). At each instance of time each chameleon performs an independent but identical coin toss experiment with probability ?? to decide whether to change its colour or not. If the coin lands head then the creature retains its colour (this is to be interpreted as a ``success''), otherwise it observes the colours and coin tosses of its two nearest neighbours and changes its colour only if, among its neighbours and including itself, the proportion of successes of the other colour is larger than the proportion of successes of its own colour. This produces a Markov chain with infinite state space. This model was studied by Chatterjee and Xu (2004) in the context of diffusion of technologies in a set-up of myopic, memoryless agents. In their work they assume different success probabilities of coin tosses according to the colour of the chameleon. In this work we consider the symmetric case where the success probability, $ \alpha $, is the same irrespective of the colour of the chameleon. We show that starting from any initial translation invariant distribution of colours the Markov chain converges to a limit of a single colour, i.e., even at the symmetric case there is no ``coexistence'' of the two colours at the limit. As a corollary we also characterize the set of all translation invariant stationary laws of this Markov chain. Moreover we show that starting with an i.i.d. colour distribution with density $ p \in [0, 1] $ of one colour (say red), the limiting distribution is all red with probability $ \Pi (\alpha, p) $ which is continuous in $p$ and for $p$ ``small'' $ \Pi (p) > p$. The last result can be interpreted as the model favours the ``underdog''.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Coexistence, Learning from neighbours, Markov chain, Random walk, Stationary distribution", } @Article{Bettinelli:2010:SLR, author = "J{\'e}r{\'e}mie Bettinelli", title = "Scaling Limits for Random Quadrangulations of Positive Genus", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "52:1594--52:1644", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-810", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/810", abstract = "We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given $g$, we consider, for every positive integer $n$, a random quadrangulation $ q_n$ uniformly distributed over the set of all rooted bipartite quadrangulations of genus $g$ with $n$ faces. We view it as a metric space by endowing its set of vertices with the graph distance. We show that, as $n$ tends to infinity, this metric space, with distances rescaled by the factor $n$ to the power of $ - 1 / 4$, converges in distribution, at least along some subsequence, toward a limiting random metric space. This convergence holds in the sense of the Gromov--Hausdorff topology on compact metric spaces. We show that, regardless of the choice of the subsequence, the Hausdorff dimension of the limiting space is almost surely equal to $4$. Our main tool is a bijection introduced by Chapuy, Marcus, and Schaeffer between the quadrangulations we consider and objects they call well-labeled $g$-trees. An important part of our study consists in determining the scaling limits of the latter.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "conditioned process; Gromov topology; random map; random tree", } @Article{Menozzi:2010:SNA, author = "St{\'e}phane Menozzi and Vincent Lemaire", title = "On Some non Asymptotic Bounds for the {Euler} Scheme", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "53:1645--53:1681", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-814", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/814", abstract = "We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This Gaussian concentration is derived from a Gaussian upper bound of the density of the scheme and a modification of the so-called ``Herbst argument'' used to prove Logarithmic Sobolev inequalities. We eventually establish a Gaussian lower bound for the density of the scheme that emphasizes the concentration is sharp.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Non asymptotic Monte Carlo bounds, Discretization schemes, Gaussian concentration", } @Article{Bhamidi:2010:SLC, author = "Shankar Bhamidi and Remco van der Hofstad and Johan van Leeuwaarden", title = "Scaling Limits for Critical Inhomogeneous Random Graphs with Finite Third Moments", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "54:1682--54:1702", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-817", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/817", abstract = "We identify the scaling limit for the sizes of the largest components at criticality for inhomogeneous random graphs with weights that have finite third moments. We show that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, which extends results of Aldous (1997) for the critical behavior of Erd{\H{o}}s--R{\'e}nyi random graphs. We rely heavily on martingale convergence techniques, and concentration properties of (super)martingales. This paper is part of a programme initiated in van der Hofstad (2009) to study the near-critical behavior in inhomogeneous random graphs of so-called rank-1.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian excursions; critical random graphs; inhomogeneous networks; martingale techniques; phase transitions; size-biased ordering", } @Article{Reinert:2010:SMS, author = "Gesine Reinert and Ivan Nourdin and Giovanni Peccati", title = "{Stein}'s Method and Stochastic Analysis of {Rademacher} Functionals", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "55:1703--55:1742", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-823", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/823", abstract = "We compute explicit bounds in the Gaussian approximation of functionals of infinite Rademacher sequences. Our tools involve Stein's method, as well as the use of appropriate discrete Malliavin operators. As the bounds are given in terms of Malliavin operators, no coupling construction is required. When the functional depends only on the first d coordinates of the Rademacher sequence, a simple sufficient condition for convergence to a normal distribution is derived. For finite quadratic forms, we obtain necessary and sufficient conditions. Although our approach does not require the classical use of exchangeable pairs, when the functional depends only on the first d coordinates of the Rademacher sequence we employ chaos expansion in order to construct an explicit exchangeable pair vector; the elements of the vector relate to the summands in the chaos decomposition and satisfy a linearity condition for the conditional expectation. Among several examples, such as random variables which depend on infinitely many Rademacher variables, we provide three main applications: (i) to CLTs for multilinear forms belonging to a fixed chaos, (ii) to the Gaussian approximation of weighted infinite 2-runs, and (iii) to the computation of explicit bounds in CLTs for multiple integrals over sparse sets. This last application provides an alternate proof (and several refinements) of a recent result by Blei and Janson.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central Limit Theorems; Discrete Malliavin operators; Normal approximation; Rademacher sequences; Sparse sets; Stein's method; Walsh chaos", } @Article{Jakubowski:2010:CDS, author = "Jecek Jakubowski and Mariusz Nieweglowski", title = "A Class of {$F$}-Doubly Stochastic {Markov} Chains", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "56:1743--56:1771", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-815", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/815", abstract = "We define a new class of processes, very useful in applications, $ \mathbf {F}$-doubly stochastic Markov chains which contains among others Markov chains. This class is fully characterized by some martingale properties, and one of them is new even in the case of Markov chains. Moreover a predictable representation theorem holds and doubly stochastic property is preserved under natural change of measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$\mathbb{F}$-doubly stochastic Markov chain; intensity; Kolmogorov equations, martingale characterization; predictable representation theorem; sojourn time", } @Article{Croydon:2010:SAS, author = "David Croydon and Benjamin Hambly", title = "Spectral Asymptotics for Stable Trees", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "57:1772--57:1801", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-819", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/819", abstract = "We calculate the mean and almost-sure leading order behaviour of the high frequency asymptotics of the eigenvalue counting function associated with the natural Dirichlet form on $ \alpha $-stable trees, which lead in turn to short-time heat kernel asymptotics for these random structures. In particular, the conclusions we obtain demonstrate that the spectral dimension of an $ \alpha $-stable tree is almost-surely equal to $ 2 \alpha / (2 \alpha - 1)$, matching that of certain related discrete models. We also show that the exponent for the second term in the asymptotic expansion of the eigenvalue counting function is no greater than $ 1 / (2 \alpha - 1)$. To prove our results, we adapt a self-similar fractal argument previously applied to the continuum random tree, replacing the decomposition of the continuum tree at the branch point of three suitably chosen vertices with a recently developed spinal decomposition for $ \alpha $-stable trees", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "heat kernel; self-similar decomposition; spectral asymptotics; stable tree", } @Article{Warfheimer:2010:SDI, author = "Marcus Warfheimer", title = "Stochastic Domination for the {Ising} and Fuzzy {Potts} Models", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "58:1802--58:1824", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-820", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/820", abstract = "We discuss various aspects concerning stochastic domination for the Ising model and the fuzzy Potts model. We begin by considering the Ising model on the homogeneous tree of degree $d$, $ \mathbb {T}^d$. For given interaction parameters $ J_1$, $ J_2 > 0$ and external field $ h_1 \in \mathbb {R}$, we compute the smallest external field $ \tilde {h}$ such that the plus measure with parameters $ J_2$ and $h$ dominates the plus measure with parameters $ J_1$ and $ h_1$ for all $ h \geq \tilde {h}$. Moreover, we discuss continuity of $ \tilde {h}$ with respect to the three parameters $ J_1$, $ J_2$, $ h_1$ and also how the plus measures are stochastically ordered in the interaction parameter for a fixed external field. Next, we consider the fuzzy Potts model and prove that on $ \mathbb {Z}^d$ the fuzzy Potts measures dominate the same set of product measures while on $ \mathbb {T}^d$, for certain parameter values, the free and minus fuzzy Potts measures dominate different product measures", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "domination of product measures; fuzzy Potts model; Ising model; Stochastic domination", } @Article{Huesler:2010:CHE, author = "Juerg Huesler and Anna Ladneva and Vladimir Piterbarg", title = "On Clusters of High Extremes of {Gaussian} Stationary Processes with $ \varepsilon $-Separation", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "59:1825--59:1862", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-828", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/828", abstract = "The clustering of extremes values of a stationary Gaussian process $ X(t), t \in [0, T] $ is considered, where at least two time points of extreme values above a high threshold are separated by at least a small positive value $ \varepsilon $. Under certain assumptions on the correlation function of the process, the asymptotic behavior of the probability of such a pattern of clusters of exceedances is derived exactly where the level to be exceeded by the extreme values, tends to $ \infty $. The excursion behaviour of the paths in such an event is almost deterministic and does not depend on the high level $u$. We discuss the pattern and the asymptotic probabilities of such clusters of exceedances.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "asymptotic behavior; clusters; correlation function; extreme values; Gaussian process; separated clusters", } @Article{Hwang:2010:MRB, author = "Hsien-Kuei Hwang and Tsung-Hsi Tsai", title = "Multivariate Records Based on Dominance", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "60:1863--60:1892", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-825", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/825", abstract = "We consider three types of multivariate records in this paper and derive the mean and the variance of their numbers for independent and uniform random samples from two prototype regions: hypercubes $ [0, 1]^d $ and d-dimensional simplex. Central limit theorems with convergence rates are established when the variance tends to infinity. Effective numerical procedures are also provided for computing the variance constants to high degree of precision.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Multivariate records, Pareto optimality, central limit theorems, {Berry--Ess{\'e}en} bound, partial orders, dominance", } @Article{Janson:2010:MBM, author = "Svante Janson and Guy Louchard and Anders Martin-L{\"o}f", title = "The Maximum of {Brownian} Motion with Parabolic Drift", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "61:1893--61:1929", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-830", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/830", abstract = "We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give new series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, parabolic drift, Airy functions", } @Article{Groeneboom:2010:MBM, author = "Piet Groeneboom", title = "The Maximum of {Brownian} Motion Minus a Parabola", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "62:1930--62:1937", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-826", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/826", abstract = "We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both for one-sided and two-sided Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, parabolic drift, maximum, Airy functions", } @Article{Englander:2010:CMS, author = "Janos Englander", title = "The Center of Mass for Spatial Branching Processes and an Application for Self-Interaction", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "63:1938--63:1970", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-822", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/822", abstract = "Consider the center of mass of a supercritical branching-Brownian motion. In this article we first show that it is a Brownian motion being slowed down such that it tends to a limiting position almost surely, and that this is also true for a model where the branching-Brownian motion is modified by attraction/repulsion between particles. We then put this observation together with the description of the interacting system as viewed from its center of mass, and get the following asymptotic behavior: the system asymptotically becomes a branching Ornstein--Uhlenbeck process (inward for attraction and outward for repulsion), but (i) the origin is shifted to a random point which has normal distribution, and (ii) the Ornstein--Uhlenbeck particles are not independent but constitute a system with a degree of freedom which is less than their number by precisely one. The main result of the article then is a scaling limit theorem for the local mass, in the attractive case. A conjecture is stated for the behavior of the local mass in the repulsive case. We also consider a supercritical super-Brownian motion. Again, it turns out that, conditioned on survival, its center of mass is a continuous process having an a.s. limit.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching Brownian motion; branching Ornstein--Uhlenbeck process; center of mass; Curie--Weiss model; H-transform; McKean--Vlasov limit; self-interaction; spatial branching processes; super-Brownian motion", } @Article{Bank:2010:PDO, author = "Peter Bank and Christoph Baumgarten", title = "Parameter-Dependent Optimal Stopping Problems for One-Dimensional Diffusions", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "64:1971--64:1993", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-835", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/835", abstract = "We consider a class of optimal stopping problems for a regular one-dimensional diffusion whose payoff depends on a linear parameter. As shown in Bank and F{\"o}llmer (2003) problems of this type may allow for a universal stopping signal that characterizes optimal stopping times for any given parameter via a level-crossing principle of some auxiliary process. For regular one-dimensional diffusions, we provide an explicit construction of this signal in terms of the Laplace transform of level passage times. Explicit solutions are available under certain concavity conditions on the reward function. In general, the construction of the signal at a given point boils down to finding the infimum of an auxiliary function of one real variable. Moreover, we show that monotonicity of the stopping signal corresponds to monotone and concave (in a suitably generalized sense) reward functions. As an application, we show how to extend the construction of Gittins indices of Karatzas (1984) from monotone reward functions to arbitrary functions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Optimal stopping, Gittins index, multi-armed bandit problems, American options, universal stopping signal", } @Article{Xu:2010:EEM, author = "Lihu Xu and Bogus{\l}aw Zegarli{\'n}ski", title = "Existence and Exponential Mixing of Infinite White $ \alpha $-Stable Systems with Unbounded Interactions", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "65:1994--65:2018", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-831", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/831", abstract = "We study an infinite white $ \alpha $-stable systems with unbounded interactions, and prove the existence of a solution by Galerkin approximation and an exponential mixing property by an $ \alpha $-stable version of gradient bounds.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Exponential mixing; Finite speed of propagation of information; Gradient bounds.; Lie bracket; White symmetric $alpha$-stable processes", } @Article{Madras:2010:TAP, author = "Neal Madras and C. Wu", title = "Trees, Animals, and Percolation on Hyperbolic Lattices", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "66:2019--66:2040", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-837", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/837", abstract = "We study lattice trees, lattice animals, and percolation on non-Euclidean lattices that correspond to regular tessellations of two- and three-dimensional hyperbolic space. We prove that critical exponents of these models take on their mean field values. Our methods are mainly combinatorial and geometric.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "critical exponents; hyperbolic geometry; hyperbolic lattice.; lattice animal; lattice tree; mean field behaviour; Percolation", } @Article{Xu:2010:MPC, author = "Jing Xu and Bo Zhang", title = "Martingale Property and Capacity under {$G$}-Framework", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "67:2041--67:2068", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-832", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/832", abstract = "The main purpose of this article is to study the symmetric martingale property and capacity defined by G-expectation introduced by Peng (cf. \url{http://arxiv.org/PS_cache/math/pdf/0601/0601035v2.pdf}) in 2006. We show that the G-capacity can not be dynamic, and also demonstrate the relationship between symmetric G-martingale and the martingale under linear expectation. Based on these results and path-wise analysis, we obtain the martingale characterization theorem for G Brownian motion without Markovian assumption. This theorem covers the Levy's martingale characterization theorem for Brownian motion, and it also gives a different method to prove Levy's theorem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Capacity; G-Brownian motion; G-expectation; Martingale characterization", } @Article{Boukhadra:2010:SSD, author = "Omar Boukhadra", title = "Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances Model", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "68:2069--68:2086", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-839", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/839", abstract = "We study models of continuous-time, symmetric random walks in random environment on the d-dimensional integer lattice, driven by a field of i.i.d random nearest-neighbor conductances bounded only from above with a power law tail near 0. We are interested in estimating the quenched asymptotic behavior of the on-diagonal heat-kernel. We show that the spectral dimension is standard when we lighten sufficiently the tails of the conductances. As an expected consequence, the same result holds for the discrete-time case.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov chains, Random walk, Random environments, Random conductances, Percolation", } @Article{Herrmann:2010:SMS, author = "Samuel Herrmann and Julian Tugaut", title = "Stationary measures for self-stabilizing processes: asymptotic analysis in the small noise limit", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "69:2087--69:2116", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-842", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/842", abstract = "Self-stabilizing diffusions are stochastic processes, solutions of nonlinear stochastic differential equation, which are attracted by their own law. This specific self-interaction leads to singular phenomenons like non uniqueness of associated stationary measures when the diffusion moves in some non convex environment (see [5]). The aim of this paper is to describe these invariant measures and especially their asymptotic behavior as the noise intensity in the nonlinear SDE becomes small. We prove in particular that the limit measures are discrete measures and point out some properties of their support which permit in several situations to describe explicitly the whole set of limit measures. This study requires essentially generalized Laplace's method approximations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "double well potential; Laplace's method; perturbed dynamical system; self-interacting diffusion; stationary measures", } @Article{Nourdin:2010:WSI, author = "Ivan Nourdin and Anthony R{\'e}veillac and Jason Swanson", title = "The weak {Stratonovich} integral with respect to fractional {Brownian} motion with {Hurst} parameter $ 1 / 6 $", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "70:2117--70:2162", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-843", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/843", abstract = "Let $B$ be a fractional Brownian motion with Hurst parameter $ H = 1 / 6$. It is known that the symmetric Stratonovich-style Riemann sums for $ \int \! g(B(s)) \, d B(s)$ do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of c{\`a}dl{\`a}g functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary It{\^o} integral with respect to a Brownian motion that is independent of $B$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractional Brownian motion; Malliavin calculus; Stochastic integration; Stratonovich integral; weak convergence", } @Article{Dufresne:2010:GDB, author = "Daniel Dufresne", title = "G distributions and the beta-gamma algebra", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "71:2163--71:2199", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-845", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/845", abstract = "This paper has four interrelated themes: (1) express Laplace and Mellin transforms of sums of positive random variables in terms of the Mellin transform of the summands; (2) show the equivalence of the two Barnes' lemmas with known properties of gamma distributions; (3) establish properties of the sum of two reciprocal gamma variables, and related results; (4) study the G distributions (whose Mellin transforms are ratios of products of gamma functions).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Barnes' lemmas; Beta distribution; beta product distribution; G distributions; gamma distribution; infinite divisibility; Macdonald's function; Mellin transforms", } @Article{Hessler:2010:ECP, author = "Martin Hessler and Johan W{\"a}stlund", title = "Edge cover and polymatroid flow problems", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "72:2200--72:2219", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-846", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/846", abstract = "In an $n$ by $n$ complete bipartite graph with independent exponentially distributed edge costs, we ask for the minimum total cost of a set of edges of which each vertex is incident to at least one. This so-called minimum edge cover problem is a relaxation of perfect matching. We show that the large $n$ limit cost of the minimum edge cover is $ W(1)^2 + 2 W(1) \approx 1.456$, where $W$ is the Lambert $W$-function. In particular this means that the minimum edge cover is essentially cheaper than the minimum perfect matching, whose limit cost is $ \pi^2 / 6 \approx 1.645$. We obtain this result through a generalization of the perfect matching problem to a setting where we impose a (poly-)matroid structure on the two vertex-sets of the graph, and ask for an edge set of prescribed size connecting independent sets.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Combinatorial optimization; Random graphs", } @Article{Valesin:2010:MCP, author = "Daniel Valesin", title = "Multitype Contact Process on Z: Extinction and Interface", journal = j-ELECTRON-J-PROBAB, volume = "15", pages = "73:2220--73:2260", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v15-836", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/836", abstract = "We consider a two-type contact process on the integers. Both types have equal finite range and supercritical infection rate. We show that a given type becomes extinct with probability 1 if and only if, in the initial configuration, it is confined to a finite interval and surrounded by infinitely many individuals of the other type. Additionally, we show that if both types are present in finite number in the initial configuration, then there is a positive probability that they are both present for all times. Finally, it is shown that, starting from the configuration in which all sites to the left of the origin are occupied by type 1 particles and all sites to the right of the origin are occupied by type 2 particles, the process defined by the size of the interface area between the two types is stochastically tight.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Interacting Particle Systems", } @Article{Alexander:2011:ELL, author = "Kenneth Alexander", title = "Excursions and Local Limit Theorems for {Bessel}-like Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "1:1--1:44", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-848", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/848", abstract = "We consider reflecting random walks on the nonnegative integers with drift of order $ 1 / x $ at height $x$. We establish explicit asymptotics for various probabilities associated to such walks, including the distribution of the hitting time of $0$ and first return time to $0$, and the probability of being at a given height at a given time (uniformly in a large range of heights.) In particular, for certain drifts inversely proportional to $x$ up to smaller-order correction terms, we show that the probability of a first return to $0$ at time $n$ decays as a certain inverse power of $n$, multiplied by a slowly varying factor that depends on the drift correction terms.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "excursion, Lamperti problem, random walk, Bessel process", } @Article{Vihola:2011:CAM, author = "Matti Vihola", title = "Can the Adaptive {Metropolis} Algorithm Collapse Without the Covariance Lower Bound?", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "2:45--2:75", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-840", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/840", abstract = "The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix, at step $ n + 1 $ , $ S_n = \mathrm {Cov}(X_1, \ldots, X_n) + \varepsilon I $, that is, the sample covariance matrix of the history of the chain plus a (small) constant $ \varepsilon > 0 $ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $ S_n$ induced by the factor $ \varepsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $ \varepsilon $ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $ S_n$ away from zero. The behaviour of $ S_n$ is studied in detail, indicating that the eigenvalues of $ S_n$ do not tend to collapse to zero in general. In dimension one, it is shown that $ S_n$ is bounded away from zero if the logarithmic target density is uniformly continuous. For a modification of the AM algorithm including an additional fixed component in the proposal distribution, the eigenvalues of $ S_n$ are shown to stay away from zero with a practically non-restrictive condition. This result implies a strong law of large numbers for super-exponentially decaying target distributions with regular contours.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "adaptive Markov chain Monte Carlo; Metropolis algorithm; stability; stochastic approximation", } @Article{Gilch:2011:AER, author = "Lorenz Gilch", title = "Asymptotic Entropy of Random Walks on Free Products", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "3:76--3:105", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-841", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/841", abstract = "Suppose we are given the free product $V$ of a finite family of finite or countable sets. We consider a transient random walk on the free product arising naturally from a convex combination of random walks on the free factors. We prove the existence of the asymptotic entropy and present three different, equivalent formulas, which are derived by three different techniques. In particular, we will show that the entropy is the rate of escape with respect to the Greenian metric. Moreover, we link asymptotic entropy with the rate of escape and volume growth resulting in two inequalities.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random Walks, Free Products, Asymptotic Entropy", } @Article{Borrello:2011:SOA, author = "Davide Borrello", title = "Stochastic Order and Attractiveness for Particle Systems with Multiple Births, Deaths and Jumps", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "4:106--4:151", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-852", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/852", abstract = "An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We give a characterization of stochastic order between different interacting particle systems in a large class of processes with births, deaths and jumps of many particles per time depending on the configuration in a general way: it consists in checking inequalities involving the transition rates. We construct explicitly the coupling that characterizes the stochastic order. As a corollary we get necessary and sufficient conditions for attractiveness. As an application, we first give the conditions on examples including reaction-diffusion processes, multitype contact process and conservative dynamics and then we improve an ergodicity result for an epidemic model.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "attractiveness; epidemic model; interacting particle systems; multitype contact process; Stochastic order", } @Article{Berestycki:2011:EGC, author = "Nathanael Berestycki", title = "Emergence of Giant Cycles and Slowdown Transition in Random Transpositions and $k$-Cycles", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "5:152--5:173", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-850", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/850", abstract = "Consider the random walk on the permutation group obtained when the step distribution is uniform on a given conjugacy class. It is shown that there is a critical time at which two phase transitions occur simultaneously. On the one hand, the random walk slows down abruptly: the acceleration (i.e., the second time derivative of the distance) drops from $0$ to $ - \infty $ at this time as $ n \to \infty $. On the other hand, the largest cycle size changes from microscopic to giant. The proof of this last result is considerably simpler and holds more generally than in a previous result of Oded Schramm for random transpositions. It turns out that in the case of random $k$-cycles, this critical time is proportional to $ 1 / [k(k - 1)]$, whereas the mixing time is known to be proportional to $ 1 / k$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random permutations", } @Article{Faraud:2011:CLT, author = "Gabriel Faraud", title = "A {Central Limit Theorem} for Random Walk in a Random Environment on a Marked {Galton--Watson} Tree", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "6:174--6:215", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-851", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/851", abstract = "Models of random walks in a random environment were introduced at first by Chernoff in 1967 in order to study biological mechanisms. The original model has been intensively studied since then and is now well understood. In parallel, similar models of random processes in a random environment have been studied. In this article we focus on a model of random walk on random marked trees, following a model introduced by R. Lyons and R. Pemantle (1992). Our point of view is a bit different yet, as we consider a very general way of constructing random trees with random transition probabilities on them. We prove an analogue of R. Lyons and R. Pemantle's recurrence criterion in this setting, and we study precisely the asymptotic behavior, under restrictive assumptions. Our last result is a generalization of a result of Y. Peres and O. Zeitouni (2006) concerning biased random walks on Galton--Watson trees.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random Walk, random environment, tree, branching random walk, central limit theorem", } @Article{Basse-OConnor:2011:IS, author = "Andreas Basse-O'Connor", title = "Integrability of Seminorms", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "7:216--7:229", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-853", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/853", abstract = "We study integrability and equivalence of $ L^p $-norms of polynomial chaos elements. Relying on known results for Banach space valued polynomials, we extend and unify integrability for seminorms results to random elements that are not necessarily limits of Banach space valued polynomials. This enables us to prove integrability results for a large class of seminorms of stochastic processes and to answer, partially, a question raised by C. Borell (1979, S{\'e}minaire de Probabilit{\'e}s, XIII, 1--3).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "chaos processes; integrability; regularly varying distributions; seminorms", } @Article{Bahadoran:2011:RSI, author = "Christophe Bahadoran and Jozsef Fritz and Katalin Nagy", title = "Relaxation Schemes for Interacting Exclusions", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "8:230--8:262", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-857", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/857", abstract = "We investigate the interaction of one-dimensional asymmetric exclusion processes of opposite speeds, where the exchange dynamics is combined with a creation-annihilation mechanism, and this asymmetric law is regularized by a nearest neighbor stirring of large intensity. The model admits hyperbolic (Euler) scaling, and we are interested in the hydrodynamic behavior of the system in a regime of shocks on the infiite line. This work is a continuation of a previous paper by Fritz and Nagy [FN06], where this question has been left open because of the lack of a suitable logarithmic Sobolev inequality. The problem is solved by extending the method of relaxation schemes to this stochastic model, the resulting a priory bound allows us to verify compensated compactness.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Hyperbolic scaling, interacting exclusions, Lax entropy pairs, compensated compactness, logarithmic Sobolev inequalities, relaxation schemes", } @Article{Shao:2011:NPM, author = "Jinghai Shao", title = "A New Probability Measure-Valued Stochastic Process with {Ferguson--Dirichlet} Process as Reversible Measure", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "9:271--9:292", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-844", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/844", abstract = "A new diffusion process taking values in the space of all probability measures over $ [0, 1] $ is constructed through Dirichlet form theory in this paper. This process is reversible with respect to the Ferguson--Dirichlet process (also called Poisson Dirichlet process), which is the reversible measure of the Fleming--Viot process with parent independent mutation. The intrinsic distance of this process is in the class of Wasserstein distances, so it's also a kind of Wasserstein diffusion. Moreover, this process satisfies the Log-Sobolev inequality.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Ferguson--Dirichlet process; Fleming--Viot process; Logarithmic Sobolev inequalities; Wasserstein diffusion", } @Article{Cerny:2011:TDR, author = "Ji{\v{r}}{\'\i} {\v{C}}ern{\'y}", title = "On Two-Dimensional Random Walk Among Heavy-Tailed Conductances", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "10:293--10:313", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-849", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/849", abstract = "We consider a random walk among unbounded random conductances on the two-dimensional integer lattice. When the distribution of the conductances has an infinite expectation and a polynomial tail, we show that the scaling limit of this process is the fractional kinetics process. This extends the results of the paper [BC10] where a similar limit statement was proved in dimension larger than two. To make this extension possible, we prove several estimates on the Green function of the process killed on exiting large balls.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractional kinetics; functional limit theorems; Random walk among random conductances; trap models", } @Article{Jacquot:2011:BSL, author = "Stephanie Jacquot and Benedek Valko", title = "Bulk Scaling Limit of the {Laguerre} Ensemble", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "11:314--11:346", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-854", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/854", abstract = "We consider the $ \beta $-Laguerre ensemble, a family of distributions generalizing the joint eigenvalue distribution of the Wishart random matrices. We show that the bulk scaling limit of these ensembles exists for all $ \beta > 0$ for a general family of parameters and it is the same as the bulk scaling limit of the corresponding $ \beta $-Hermite ensemble.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random matrices, eigenvalues, Laguerre ensemble, Wishart ensemble, bulk scaling limit", } @Article{Hwang:2011:CLT, author = "Hsien-Kuei Hwang and Svante Janson", title = "A {Central Limit Theorem} for Random Ordered Factorizations of Integers", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "12:347--12:361", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-858", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See erratum \cite{Hwang:2013:ECL}.", URL = "http://ejp.ejpecp.org/article/view/858", abstract = "Write an integer as finite products of ordered factors belonging to a given subset $ \mathcal {P} $ of integers larger than one. A very general central limit theorem is derived for the number of ordered factors in random factorizations for any subset $ \mathcal {P} $ containing at least two elements. The method of proof is very simple and relies in part on Delange's Tauberian theorems and an interesting Tauberian technique for handling Dirichlet series associated with odd centered moments.\par {\bf An erratum is available in \url{https://doi.org/10.1214/EJP.v18-2297} EJP volume {\bf 18} paper 16}", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "asymptotic normality; Dirichlet series; method of moments; ordered factorizations; Tauberian theorems", } @Article{Bierme:2011:CLT, author = "Hermine Bierm{\'e} and Aline Bonami and Jos{\'e} R. Leon", title = "{Central Limit Theorems} and Quadratic Variations in Terms of Spectral Density", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "13:362--13:395", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-862", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/862", abstract = "We give a new proof and provide new bounds for the speed of convergence in the Central Limit Theorem of Breuer Major on stationary Gaussian time series, which generalizes to particular triangular arrays. Our assumptions are given in terms of the spectral density of the time series. We then consider generalized quadratic variations of Gaussian fields with stationary increments under the assumption that their spectral density is asymptotically self-similar and prove Central Limit Theorems in this context.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central limit theorem; fractional Brownian Motion; Gaussian stationary process; periodogram; quadratic variations; spectral density", } @Article{Berard:2011:SPB, author = "Jean B{\'e}rard and Jean-Baptiste Gou{\'e}r{\'e}", title = "Survival Probability of the Branching Random Walk Killed Below a Linear Boundary", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "14:396--14:418", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-861", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/861", abstract = "We give an alternative proof of a result by N. Gantert, Y. Hu and Z. Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and bounded random walk steps. Connections with the Brunet--Derrida theory of stochastic fronts are discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching random walks; survival probability", } @Article{Lubetzky:2011:EEC, author = "Eyal Lubetzky and Allan Sly", title = "Explicit Expanders with Cutoff Phenomena", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "15:419--15:435", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-869", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/869", abstract = "The cutoff phenomenon describes a sharp transition in the convergence of an ergodic finite Markov chain to equilibrium. Of particular interest is understanding this convergence for the simple random walk on a bounded-degree expander graph. The first example of a family of bounded-degree graphs where the random walk exhibits cutoff in total-variation was provided only very recently, when the authors showed this for a typical random regular graph. However, no example was known for an explicit (deterministic) family of expanders with this phenomenon. Here we construct a family of cubic expanders where the random walk from a worst case initial position exhibits total-variation cutoff. Variants of this construction give cubic expanders without cutoff, as well as cubic graphs with cutoff at any prescribed time-point.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cutoff phenomenon; Expander graphs; Explicit constructions; Random walks", } @Article{Tribe:2011:SOM, author = "Roger Tribe and Nicholas Woodward", title = "Stochastic Order Methods Applied to Stochastic Travelling Waves", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "16:436--16:469", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-868", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/868", abstract = "This paper considers some one dimensional reaction diffusion equations driven by a one dimensional multiplicative white noise. The existence of a stochastic travelling wave solution is established, as well as a sufficient condition to be in its domain of attraction. The arguments use stochastic ordering techniques.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "travelling wave, stochastic order, stochastic partial differential equation", } @Article{Doring:2011:NDA, author = "Leif D{\"o}ring and Mladen Savov", title = "(Non)Differentiability and Asymptotics for Potential Densities of Subordinators", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "17:470--17:503", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-860", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/860", abstract = "For subordinators with positive drift we extend recent results on the structure of the potential measures and the renewal densities. Applying Fourier analysis a new representation of the potential densities is derived from which we deduce asymptotic results and show how the atoms of the L{\'e}vy measure translate into points of (non)differentiability of the potential densities.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Levy process, Subordinator, Creeping Probability, Renewal Density, Potential Measure", } @Article{Pascu:2011:MCR, author = "Mihai Pascu", title = "Mirror Coupling of Reflecting {Brownian} Motion and an Application to {Chavel}'s Conjecture", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "18:504--18:530", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-859", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/859", abstract = "In a series of papers, Burdzy et al. introduced the {\em mirror coupling} of reflecting Brownian motions in a smooth bounded domain $ D \subset \mathbb {R}^d $, and used it to prove certain properties of eigenvalues and eigenfunctions of the Neumann Laplacian on $D$. In the present paper we show that the construction of the mirror coupling can be extended to the case when the two Brownian motions live in different domains $ D_1, D_2 \subset \mathbb {R}^d$. As applications of the construction, we derive a unifying proof of the two main results concerning the validity of Chavel's conjecture on the domain monotonicity of the Neumann heat kernel, due to I. Chavel ([12]), respectively W. S. Kendall ([16]), and a new proof of Chavel's conjecture for domains satisfying the ball condition, such that the inner domain is star-shaped with respect to the center of the ball.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "couplings, mirror coupling, reflecting Brownian motion, Chavel's conjecture", } @Article{Osekowski:2011:SSI, author = "Adam Osekowski", title = "Sharp and Strict {$ L^p $}-Inequalities for {Hilbert}-Space-Valued Orthogonal Martingales", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "19:531--19:551", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-865", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/865", abstract = "The paper contains the proofs of sharp moment estimates for Hilbert-space valued martingales under the assumptions of differential subordination and orthogonality. The results generalize those obtained by Banuelos and Wang. As an application, we sharpen an inequality for stochastic integrals with respect to Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "best constants; Brownian motion; differential subordination; Martingale; moment inequality; orthogonal martingales; stochastic integral", } @Article{Birkner:2011:CLT, author = "Matthias Birkner and Andreas Greven and Frank den Hollander", title = "Collision Local Time of Transient Random Walks and Intermediate Phases in Interacting Stochastic Systems", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "20:552--20:586", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-878", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/878", abstract = "In a companion paper (M. Birkner, A. Greven, F. den Hollander, Quenched LDP for words in a letter sequence, {\em Probab. Theory Relat. Fields} {\bf 148}, no. 3/4 (2010), 403-456), a quenched large deviation principle (LDP) has been established for the empirical process of words obtained by cutting an i.i.d. sequence of letters into words according to a renewal process. We apply this LDP to prove that the radius of convergence of the generating function of the collision local time of two independent copies of a symmetric and strongly transient random walk on $ \mathbb {Z}^d $, $ d \geq 1 $ , both starting from the origin, strictly increases when we condition on one of the random walks, both in discrete time and in continuous time. We conjecture that the same holds when the random walk is transient but not strongly transient. The presence of these gaps implies the existence of an {\em intermediate phase\/} for the long-time behaviour of a class of coupled branching processes, interacting diffusions, respectively, directed polymers in random environments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walks, collision local time, annealed vs. quenched, large deviation principle, interacting stochastic systems, intermediate phase", } @Article{Avena:2011:LLN, author = "Luca Avena and Frank den Hollander and Frank Redig", title = "Law of Large Numbers for a Class of Random Walks in Dynamic Random Environments", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "21:587--21:617", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-866", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/866", abstract = "In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the right/left. We adapt a regeneration-time argument originally developed by Comets and Zeitouni for static random environments to prove that, under a space-time mixing property for the dynamic random environment called cone-mixing, the random walk has an a.s. constant global speed. In addition, we show that if the dynamic random environment is exponentially mixing in space-time and the local drifts are small, then the global speed can be written as a power series in the size of the local drifts. From the first term in this series the sign of the global speed can be read off. The results can be easily extended to higher dimensions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walk, dynamic random environment", } @Article{Kliem:2011:CRC, author = "Sandra Kliem", title = "Convergence of Rescaled Competing Species Processes to a Class of {SPDEs}", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "22:618--22:657", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-870", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/870", abstract = "One can construct a sequence of rescaled perturbations of voter processes in dimension $ d = 1 $ whose approximate densities are tight. By combining both long-range models and fixed kernel models in the perturbations and considering the critical long-range case, results of Cox and Perkins (2005) are refined. As a special case we are able to consider rescaled Lotka--Volterra models with long-range dispersal and short-range competition. In the case of long-range interactions only, the approximate densities converge to continuous space time densities which solve a class of SPDEs (stochastic partial differential equations), namely the heat equation with a class of drifts, driven by Fisher--Wright noise. If the initial condition of the limiting SPDE is integrable, weak uniqueness of the limits follows. The results obtained extend the results of Mueller and Tribe (1995) for the voter model by including perturbations. In particular, spatial versions of the Lotka--Volterra model as introduced in Neuhauser and Pacala (1999) are covered for parameters approaching one. Their model incorporates a fecundity parameter and models both intra- and interspecific competition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "long-range limits; Lotka--Volterra model; spatial competition; stochastic partial differential equations; Voter model", } @Article{Hairer:2011:THU, author = "Martin Hairer and Jonathan Mattingly", title = "A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic {PDEs}", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "23:658--23:738", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-875", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/875", abstract = "We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with ``polynomial'' nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if H{\"o}rmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operator $ M(t) $ can be obtained. Informally, this bound can be read as ``Fix any finite-dimensional projection $ \Pi $ on a subspace of sufficiently regular functions. Then the eigenfunctions of $ M(t) $ with small eigenvalues have only a very small component in the image of $ \Pi $.''\par We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced by Hairer and Mattingly in {\em Ann. of Math. (2) 164 (2006)}.\par One of the main novel technical tools is an almost sure bound from below on the size of ``Wiener polynomials, '' where the coefficients are possibly non-adapted stochastic processes satisfying a Lipschitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context.\par We conclude by showing that the two-dimensional stochastic Navier--Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Hypoellipticity; H{\"o}rmander condition; stochastic PDE", } @Article{Lifshits:2011:RGS, author = "Mikhail Lifshits and Werner Linde", title = "Random {Gaussian} Sums on Trees", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "24:739--24:763", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-871", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/871", abstract = "Let $T$ be a tree with induced partial order. We investigate a centered Gaussian process $X$ indexed by $T$ and generated by weight functions. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of $X$ in terms of compactness properties of $ (T, d)$. Here $d$ is a special metric defined by the weights, which, in general, is not comparable with the Dudley metric generated by $X$. In a second part we investigate the boundedness of $X$ for the binary tree. Assuming some mild regularity assumptions about on weight, we completely characterize homogeneous weights with $X$ being a.s. bounded.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian processes, processes indexed by trees, bounded processes, summation on trees, metric entropy", } @Article{Fukasawa:2011:AAS, author = "Masaaki Fukasawa", title = "Asymptotic Analysis for Stochastic Volatility: Edgeworth Expansion", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "25:764--25:791", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-879", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/879", abstract = "The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black--Scholes price and is uniform in bounded payoff functions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean reverting stochastic volatility model.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "ergodic diffusion; fast mean reverting; implied volatility", } @Article{Lucon:2011:QLF, author = "Eric Lu{\c{c}}on", title = "Quenched Limits and Fluctuations of the Empirical Measure for Plane Rotators in Random Media", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "26:792--26:829", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-874", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/874", abstract = "The Kuramoto model has been introduced to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. The model consists of $N$ interacting oscillators on the one dimensional sphere $ S^1$, driven by independent Brownian Motions with constant drift chosen at random. This quenched disorder is chosen independently for each oscillator according to the same law $ \mu $. The behaviour of the system for large $N$ can be understood via its empirical measure: we prove here the convergence as $ N \to \infty $ of the quenched empirical measure to the unique solution of coupled McKean--Vlasov equations, under weak assumptions on the disorder $ \mu $ and general hypotheses on the interaction. The main purpose of this work is to address the issue of quenched fluctuations around this limit, motivated by the dynamical properties of the disordered system for large but fixed $N$: hence, the main result of this paper is a quenched Central Limit Theorem for the empirical measure. Whereas we observe a self-averaging for the law of large numbers, this no longer holds for the corresponding central limit theorem: the trajectories of the fluctuations process are sample-dependent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem; disordered systems; Kuramoto model; quenched fluctuations; Synchronization", } @Article{Fan:2011:RTG, author = "ShengJun Fan and Long Jiang and YingYing Xu", title = "Representation Theorem for Generators of {BSDEs} with Monotonic and Polynomial-Growth Generators in the Space of Processes", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "27:830--27:844", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-873", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/873", abstract = "In this paper, on the basis of some recent works of Fan, Jiang and Jia, we establish a representation theorem in the space of processes for generators of BSDEs with monotonic and polynomial-growth generators, which generalizes the corresponding results in Fan (2006, 2007), and Fan and Hu (2008).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Backward stochastic differential equation; Monotonic generator; Polynomial-growth generator; Representation theorem of generators", } @Article{Andres:2011:PDS, author = "Sebastian Andres", title = "Pathwise Differentiability for {SDEs} in a Smooth Domain with Reflection", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "28:845--28:879", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-872", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/872", abstract = "In this paper we study a Skorohod SDE in a smooth domain with normal reflection at the boundary, in particular we prove that the solution is pathwise differentiable with respect to the deterministic starting point. The resulting derivatives evolve according to an ordinary differential equation, when the process is in the interior of the domain, and they are projected to the tangent space, when the process hits the boundary.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "local time; normal reflection; Stochastic differential equation with reflection", } @Article{Barbour:2011:ADD, author = "Andrew Barbour and Bruno Nietlispach", title = "Approximation by the {Dickman} Distribution and Quasi-Logarithmic Combinatorial Structures", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "29:880--29:902", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-881", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/881", abstract = "Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavar{\'e} (2003). In order to obtain asymptotic approximations to their component spectrum, it is necessary first to establish an approximation to the sum of an associated sequence of independent random variables in terms of the Dickman distribution. This in turn requires an argument that refines the Mineka coupling by incorporating a blocking construction, leading to exponentially sharper coupling rates for the sums in question. Applications include distributional limit theorems for the size of the largest component and for the vector of counts of the small components in a quasi-logarithmic combinatorial structure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dickman's distribution; Logarithmic combinatorial structures; Mineka coupling", } @Article{Chen:2011:MTA, author = "Che-Hao Chen and Michael Fuchs", title = "On the Moment-Transfer Approach for Random Variables Satisfying a One-Sided Distributional Recurrence", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "30:903--30:928", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-885", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/885", abstract = "The moment-transfer approach is a standard tool for deriving limit laws of sequences of random variables satisfying a distributional recurrence. However, so far the approach could not be applied to certain ``one-sided'' recurrences with slowly varying moments and normal limit law. In this paper, we propose a modified version of the moment-transfer approach which can be applied to such recurrences. Moreover, we demonstrate the usefulness of our approach by re-deriving several recent results in an almost automatic fashion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "analysis of algorithms; central limit theorem; distributional recurrence; moment-transfer approach", } @Article{Fisher:2011:SSD, author = "Albert Fisher and Marina Talet", title = "The Self-Similar Dynamics of Renewal Processes", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "31:929--31:961", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-888", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/888", abstract = "We prove an almost sure invariance principle in log density for renewal processes with gaps in the domain of attraction of an $ \alpha $-stable law. There are three different types of behavior: attraction to a Mittag-Leffler process for $ 0 < \alpha < 1$, to a centered Cauchy process for $ \alpha = 1$ and to a stable process for $ 1 < \alpha \leq 2$. Equivalently, in dynamical terms, almost every renewal path is, upon centering and up to a regularly varying coordinate change of order one, and after removing a set of times of Ces{\`a}ro density zero, in the stable manifold of a self-similar path for the scaling flow. As a corollary we have pathwise functional and central limit theorems.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stable process, renewal process, Mittag-Leffler process, Cauchy process, almost-sure invariance principle in log density, pathwise Central Limit Theorem", } @Article{Liu:2011:HFK, author = "Gi-Ren Liu and Narn-Rueih Shieh", title = "Homogenization of Fractional Kinetic Equations with Random Initial Data", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "32:962--32:980", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-896", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/896", abstract = "We present the small-scale limits for the homogenization of a class of spatial-temporal random fields; the field arises from the solution of a certain fractional kinetic equation and also from that of a related two-equation system, subject to given random initial data. The space-fractional derivative of the equation is characterized by the composition of the inverses of the Riesz potential and the Bessel potential. We discuss the small-scale (the micro) limits, opposite to the well-studied large-scale limits, of such spatial-temporal random field. Our scaling schemes involve both the Riesz and the Bessel parameters, and also involve the rescaling in the initial data; our results are completely new-type scaling limits for such random fields.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Hermite expansion; Homogenization; Long-range dependence; Multiple It{\^o}-Wiener integral; Random initial data; Riesz--Bessel fractional equation and system; Small-scale limits", } @Article{Zerner:2011:IP, author = "Martin Zerner", title = "Interpolation Percolation", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "33:981--33:1000", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-895", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/895", abstract = "Let $X$ be a countably infinite set of real numbers and let $ (Y_x)_{x \in X}$ be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the almost sure existence of various ``regular'' functions f with the property that $ f(x) \in Y_x$ for all $ x \in X$. Several open questions are posed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Interpolation, path connected, percolation, stationary random set", } @Article{Stadje:2011:TKG, author = "Wolfgang Stadje and Achim W{\"u}bker", title = "Three Kinds of Geometric Convergence for {Markov} Chains and the Spectral Gap Property", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "34:1001--34:1019", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-900", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/900", abstract = "In this paper we investigate three types of convergence for geometrically ergodic Markov chains (MCs) with countable state space, which in general lead to different `rates of convergence'. For reversible Markov chains it is shown that these rates coincide. For general MCs we show some connections between their rates and those of the associated reversed MCs. Moreover, we study the relations between these rates and a certain family of isoperimetric constants. This sheds new light on the connection of geometric ergodicity and the so-called spectral gap property, in particular for non-reversible MCs, and makes it possible to derive sharp upper and lower bounds for the spectral radius of certain non-reversible chains", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov chains, geometric ergodicity, speed of convergence", } @Article{Munsonius:2011:AIP, author = "Goetz Olaf Munsonius", title = "On the Asymptotic Internal Path Length and the Asymptotic {Wiener} Index of Random Split Trees", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "35:1020--35:1047", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-889", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/889", abstract = "The random split tree introduced by Devroye (1999) is considered. We derive a second order expansion for the mean of its internal path length and furthermore obtain a limit law by the contraction method. As an assumption we need the splitter having a Lebesgue density and mass in every neighborhood of 1. We use properly stopped homogeneous Markov chains, for which limit results in total variation distance as well as renewal theory are used. Furthermore, we extend this method to obtain the corresponding results for the Wiener index.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "internal path length; probabilistic analysis of algorithms; random trees; Wiener index", } @Article{Adler:2011:PAP, author = "Mark Adler and Mattia Cafasso and Pierre van Moerbeke", title = "From the {Pearcey} to the {Airy} Process", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "36:1048--36:1064", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-898", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/898", abstract = "Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's dynamics, then leads to interesting, infinite-dimensional diffusions for the eigenvalues. This paper studies the relationship between two of the models, namely the Airy and Pearcey processes and more precisely shows how to approximate the multi-time statistics for the Pearcey process by the one of the Airy process with the help of a PDE governing the gap probabilities for the Pearcey process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Airy process; Dyson's Brownian motions.; Pearcey process", } @Article{Adamczak:2011:MPC, author = "Radoslaw Adamczak", title = "On the {Marchenko--Pastur} and Circular Laws for some Classes of Random Matrices with Dependent Entries", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "37:1065--37:1095", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-899", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/899", abstract = "In the first part of the article we prove limit theorems of Marchenko--Pastur type for the average spectral distribution of random matrices with dependent entries satisfying a weak law of large numbers, uniform bounds on moments and a martingale like condition investigated previously by Goetze and Tikhomirov. Examples include log-concave unconditional distributions on the space of matrices. In the second part we specialize to random matrices with independent isotropic unconditional log-concave rows for which (using the Tao-Vu replacement principle) we prove the circular law.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random matrix, Marchenko--Pastur law, circular law, log-concave measures", } @Article{Zhang:2011:SHF, author = "Xicheng Zhang", title = "Stochastic Homeomorphism Flows of {SDEs} with Singular Drifts and {Sobolev} Diffusion Coefficients", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "38:1096--38:1116", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-887", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/887", abstract = "In this paper we prove the stochastic homeomorphism flow property and the strong Feller property for stochastic differential equations with singular time dependent drifts and Sobolev diffusion coefficients. Moreover, the local well posedness under local assumptions are also obtained. In particular, we extend Krylov and R{\"o}ckner's results in [10] to the case of non-constant diffusion coefficients.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic homoemorphism flow, Strong Feller property, Singular drift, Krylov's estimates, Zvonkin's transformation", } @Article{Bouzar:2011:DSS, author = "Nadjib Bouzar", title = "Discrete Semi-Self-Decomposability Induced by Semigroups", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "39:1117--39:1133", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-890", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/890", abstract = "A continuous semigroup of probability generating functions $ \mathcal {F} := (F_t, t \ge 0) $ is used to introduce a notion of discrete semi-selfdecomposability, or $ \mathcal {F}$-semi-selfdecomposability, for distributions with support on $ \bf Z_+$. $ \mathcal {F}$-semi-selfdecomposable distributions are infinitely divisible and are characterized by the absolute monotonicity of a specific function. The class of $ \mathcal {F}$-semi-selfdecomposable laws is shown to contain the $ \mathcal {F}$- semistable distributions and the geometric $ \mathcal {F}$-semistable distributions. A generalization of discrete random stability is also explored.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "composition semigroups, discrete distributions, infinite divisibility, semi-stability, Markov branching processes, weak convergence", } @Article{Leonenko:2011:FEH, author = "Nikolai Leonenko and Maria D. Ruiz-Medina and Murad S. Taqqu", title = "Fractional Elliptic, Hyperbolic and Parabolic Random Fields", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "40:1134--40:1172", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-891", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/891", abstract = "This paper introduces new classes of fractional and multifractional random fields arising from elliptic, parabolic and hyperbolic equations with random innovations derived from fractional Brownian motion. The case of stationary random initial conditions is also considered for parabolic and hyperbolic equations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cylindrical fractional Brownian, motion; elliptic, hyperbolic, parabolic random fields; fractional Bessel potential spaces; fractional Holder spaces; fractional random fields; multifractional random fields; spectral representation", } @Article{Betz:2011:SRP, author = "Volker Betz and Daniel Ueltschi", title = "Spatial Random Permutations and {Poisson--Dirichlet} Law of Cycle Lengths", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "41:1173--41:1192", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-901", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/901", abstract = "We study spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and their cycle lengths satisfy a Poisson--Dirichlet law.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Spatial random permutations, cycle weights, Poisson--Dirichlet distribution", } @Article{Dimitroff:2011:AEB, author = "Georgi Dimitroff and Michael Scheutzow", title = "Attractors and Expansion for {Brownian} Flows", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "42:1193--42:1213", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-894", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/894", abstract = "We show that a stochastic flow which is generated by a stochastic differential equation on $ \mathbb {R}^d $ with bounded volatility has a random attractor provided that the drift component in the direction towards the origin is larger than a certain strictly positive constant $ \beta $ outside a large ball. Using a similar approach, we provide a lower bound for the linear growth rate of the inner radius of the image of a large ball under a stochastic flow in case the drift component in the direction away from the origin is larger than a certain strictly positive constant $ \beta $ outside a large ball. To prove the main result we use {\em chaining techniques} in order to control the growth of the diameter of subsets of the state space under the flow.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "attractor; chaining; stochastic differential equation; Stochastic flow", } @Article{Kolb:2011:SGB, author = "Martin Kolb and Achim W{\"u}bker", title = "On the Spectral Gap of {Brownian} Motion with Jump Boundary", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "43:1214--43:1237", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-903", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/903", abstract = "In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are different and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, coupling; jump-boundary; jump-process; spectral gap; spectral gap property; speed of convergence", } @Article{Deijfen:2011:SPG, author = "Maria Deijfen and Alexander Holroyd and Yuval Peres", title = "Stable {Poisson} Graphs in One Dimension", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "44:1238--44:1253", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-897", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/897", abstract = "Let each point of a homogeneous Poisson process on R independently be equipped with a random number of stubs (half-edges) according to a given probability distribution $ \mu $ on the positive integers. We consider schemes based on Gale--Shapley stable marriage for perfectly matching the stubs to obtain a simple graph with degree distribution $ \mu $. We prove results on the existence of an infinite component and on the length of the edges, with focus on the case $ \mu (2) = 1 $. In this case, for the random direction stable matching scheme introduced by Deijfen and Meester we prove that there is no infinite component, while for the stable matching of Deijfen, H{\"a}ggstr{\"o}m and Holroyd we prove that existence of an infinite component follows from a certain statement involving a {\em finite} interval, which is overwhelmingly supported by simulation evidence", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "degree distribution; matching; percolation; Poisson process; random graph", } @Article{Huesler:2011:EGP, author = "Juerg Huesler and Vladimir Piterbarg and Yueming Zhang", title = "Extremes of {Gaussian} Processes with Random Variance", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "45:1254--45:1280", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-904", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/904", abstract = "Let $ \xi (t) $ be a standard locally stationary Gaussian process with covariance function $ 1 - r(t, t + s) \sim C(t)|s|^\alpha $ as $ s \to 0 $, with $ 0 < \alpha \leq 2 $ and $ C(t) $ a positive bounded continuous function. We are interested in the exceedance probabilities of $ \xi (t) $ with a random standard deviation $ \eta (t) = \eta - \zeta t^\beta $, where $ \eta $ and $ \zeta $ are non-negative bounded random variables. We investigate the asymptotic behavior of the extreme values of the process $ \xi (t) \eta (t) $ under some specific conditions which depends on the relation between $ \alpha $ and $ \beta $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "extremes; fractional Brownian motions; Gaussian processes; locally stationary; random variance; ruin probability", } @Article{Jonasson:2011:MTB, author = "Johan Jonasson", title = "Mixing Time Bounds for Overlapping Cycles Shuffles", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "46:1281--46:1295", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-912", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/912", abstract = "Consider a deck of $n$ cards. Let $ p_1, p_2, \ldots, p_n $ be a probability vector and consider the mixing time of the card shuffle which at each step of time picks a position according to the $ p_i$'s and move the card in that position to the top. This setup was introduced in [5], where a few special cases were studied. In particular the case $ p_{n - k} = p_n = 1 / 2 $, $ k = \Theta (n) $, turned out to be challenging and only a few lower bounds were produced. These were improved in [1] where it was shown that the relaxation time for the motion of a single card is $ \Theta (n^2) $ when $ k / n $ approaches a rational number. In this paper we give the first upper bounds. We focus on the case $ m := n - k = \lfloor n / 2 \rfloor $. It is shown that for the additive symmetrization as well as the lazy version of the shuffle, the mixing time is $ O(n^3 \log (n)) $. We then consider two other modifications of the shuffle. The first one is the case $ p_{n - k} = p_{n - k + 1} = 1 / 4 $ and $ p_n = 1 / 2 $. Using the entropy technique developed by Morris [7], we show that mixing time is $ O(n^2 \log^3 (n)) $ for the shuffle itself as well as for the symmetrization. The second modification is a variant of the first, where the moves are made in pairs so that if the first move involves position $n$ , then the second move must be taken from positions $m$ or $ m + 1$ and vice versa. Interestingly, this shuffle is much slower; the mixing time is at least of order $ n^3 \log (n)$ and at most of order $ n^3 \log^3 (n))$. It is also observed that results of [1] can be modified to improve lower bounds for some $ k = o(n)$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "comparison technique, Wilson's technique, relative entropy", } @Article{Kijung:2011:TSP, author = "Lee Kijung and Kim Kyeong-Hun", title = "A {$ W^1_2 $}-Theory of Stochastic Partial Differential Systems of Divergence Type on {$ C^1 $} Domains", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "47:1296--47:1317", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-913", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/913", abstract = "In this paper we study the stochastic partial differential systems of divergence type with $ \mathcal {C}^1 $ space domains in $ \mathbb {R}^d $. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solution to blow up near the boundary. The coefficients of the systems are only measurable and are allowed to blow up near the boundary.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic parabolic partial differential systems, divergence type, weighted Sobolev spaces", } @Article{Heil:2011:BRW, author = "Hadrian Heil and Nakashima Makoto and Yoshida Nobuo", title = "Branching Random Walks in Random Environment are Diffusive in the Regular Growth Phase", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "48:1318--48:1340", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-922", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/922", abstract = "We treat branching random walks in random environment using the framework of Linear Stochastic Evolution. In spatial dimensions three or larger, we establish diusive behaviour in the entire growth phase. This can be seen through a Central Limit Theorem with respect to the population density as well as through an invariance principle for a path measure we introduce.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching random walk, random environment, central limit theorem, invariance principle, di", } @Article{Chen:2011:SSC, author = "Xinxing Chen and Dayue Chen", title = "Some Sufficient Conditions for Infinite Collisions of Simple Random Walks on a Wedge Comb", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "49:1341--49:1355", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-907", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/907", abstract = "In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile $ \{ f(n) \colon n \in \mathbb {Z} \} $. One interesting result is that two independent simple random walks on the wedge comb will collide infinitely many times if $ f(n) $ has a growth order as $ n \log (n) $. On the other hand, if $ \{ f(n) \colon n \in \mathbb {Z} \} $ are given by i.i.d. non-negative random variables with finite mean, then for almost all wedge combs with such profile, three independent simple random walks on it will collide infinitely many times", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "wedge comb, simple random walk, infinite collision property, local time", } @Article{Kevei:2011:CMB, author = "Peter Kevei and Jose Lopez Mimbela", title = "Critical Multitype Branching Systems: Extinction Results", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "50:1356--50:1380", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-908", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/908", abstract = "We consider a critical branching particle system in $ \mathbb {R}^d $, composed of individuals of a finite number of types $ i \in \{ 1, \ldots, K \} $. Each individual of type i moves independently according to a symmetric $ \alpha_i$-stable motion. We assume that the particle lifetimes and offspring distributions are type-dependent. Under the usual independence assumptions in branching systems, we prove extinction theorems in the following cases: (1) all the particle lifetimes have finite mean, or (2) there is a type whose lifetime distribution has heavy tail, and the other lifetimes have finite mean. We get a more complex dynamics by assuming in case (2) that the most mobile particle type corresponds to a finite-mean lifetime: in this case, local extinction of the population is determined by an interaction of the parameters (offspring variability, mobility, longevity) of the long-living type and those of the most mobile type. The proofs are based on a precise analysis of the occupation times of a related Markov renewal process, which is of independent interest.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Critical branching particle system; Extinction; Markov renewal process", } @Article{Pekoz:2011:EAN, author = "Erol Pek{\"o}z and Adrian R{\"o}llin", title = "Exponential Approximation for the Nearly Critical {Galton--Watson} Process and Occupation Times of {Markov} Chains", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "51:1381--51:1393", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-914", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/914", abstract = "In this article we provide new applications for exponential approximation using the framework of Pek{\"o}z and R{\"o}llin (2011), which is based on Stein's method. We give error bounds for the nearly critical Galton--Watson process conditioned on non-extinction, and for the occupation times of Markov chains; for the latter, in particular, we give a new exponential approximation rate for the number of revisits to the origin for general two dimensional random walk, also known as the Erd{\H{o}}s--Taylor theorem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Erd{\H{o}}s--Taylor theorem; Exponential distribution; nearly critical Galton--Watson branching process; occupation times of Markov chains; Stein's method", } @Article{Knopova:2011:EAD, author = "Victoria Knopova and Alexei Kulik", title = "Exact Asymptotic for Distribution Densities of {L{\'e}vy} Functionals", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "52:1394--52:1433", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-909", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/909", abstract = "A version of the saddle point method is developed, which allows one to describe exactly the asymptotic behavior of distribution densities of L{\'e}vy driven stochastic integrals with deterministic kernels. Exact asymptotic behavior is established for (a) the transition probability density of a real-valued L{\'e}vy process; (b) the transition probability density and the invariant distribution density of a L{\'e}vy driven Ornstein--Uhlenbeck process; (c) the distribution density of the fractional L{\'e}vy motion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "L'evy process, L'evy driven Ornstein--Uhlenbeck process, transition distribution density, saddle point method, Laplace method", } @Article{Lim:2011:EUM, author = "Thomas Lim and Marie-Claire Quenez", title = "Exponential Utility Maximization in an Incomplete Market with Defaults", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "53:1434--53:1464", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-918", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/918", abstract = "In this paper, we study the exponential utility maximization problem in an incomplete market with a default time inducing a discontinuity in the price of stock. We consider the case of strategies valued in a closed set. Using dynamic programming and BSDEs techniques, we provide a characterization of the value function as the maximal subsolution of a backward stochastic differential equation (BSDE) and an optimality criterium. Moreover, in the case of bounded coefficients, the value function is shown to be the maximal solution of a BSDE. Moreover, the value function can be written as the limit of a sequence of processes which can be characterized as the solutions of Lipschitz BSDEs in the case of bounded coefficients. In the case of convex constraints and under some exponential integrability assumptions on the coefficients, some complementary properties are provided. These results can be generalized to the case of several default times or a Poisson process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "backward stochastic di; default time; dynamic programming; exponential utility; incomplete market; Optimal investment", } @Article{Backhausz:2011:LDD, author = "Agnes Backhausz and Tamas Mori", title = "Local Degree Distribution in Scale Free Random Graphs", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "54:1465--54:1488", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-916", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/916", abstract = "In several scale free graph models the asymptotic degree distribution and the characteristic exponent change when only a smaller set of vertices is considered. Looking at the common properties of these models, we present sufficient conditions for the almost sure existence of an asymptotic degree distribution constrained to the set of selected vertices, and identify the chararteristic exponent belonging to it.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "martingales; random graphs; recursive trees; regular variation; scale free", } @Article{Deya:2011:DAR, author = "Aur{\'e}lien Deya", title = "A Discrete Approach to Rough Parabolic Equations", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "55:1489--55:1518", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-919", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/919", abstract = "By combining the formalism of [8] with a discrete approach close to the considerations of [6], we interpret and we solve the rough partial differential equation\par $$ d y_t = A y_t d t + \sum_{i = 1}^m f_i(y_t)d x_t^i, t \in [0, T] $$ on a compact domain $ \mathcal {O} $ of $ \mathbb {R}^n $, where $A$ is a rather general elliptic operator of $ L^p(\mathcal {O})$, $ p > 1$, and $ f_i(\varphi)(\xi) = f_i(\varphi (\xi))$, and $x$ is the generator of a 2-rough path. The (global) existence, uniqueness and continuity of a solution is established under classical regularity assumptions for $ f_i$. Some identification procedures are also provided in order to justify our interpretation of the problem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Fractional Brownian motion; Rough paths theory; Stochastic PDEs", } @Article{Gartner:2011:TCP, author = "J{\"u}rgen G{\"a}rtner and Adrian Schnitzler", title = "Time Correlations for the Parabolic {Anderson} Model", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "56:1519--56:1548", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-917", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/917", abstract = "We derive exact asymptotics of time correlation functions for the parabolic Anderson model with homogeneous initial condition and time-independent tails that decay more slowly than those of a double exponential distribution and have a finite cumulant generating function. We use these results to give precise asymptotics for statistical moments of positive order. Furthermore, we show what the potential peaks that contribute to the intermittency picture look like and how they are distributed in space. We also investigate for how long intermittency peaks remain relevant in terms of ageing properties of the model.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "ageing; Anderson Hamiltonian; annealed asymptotics; intermittency; Parabolic Anderson model; random potential; time correlations", } @Article{Jordan:2011:RRG, author = "Jonathan Jordan", title = "Randomised Reproducing Graphs", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "57:1549--57:1562", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-921", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/921", abstract = "We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random element, and there are three parameters, $ \alpha $, $ \beta $ and $ \gamma $, which are the probabilities of edges appearing between different types of vertices. We show that as the probabilities associated with the model vary there are a number of phase transitions, in particular concerning the degree sequence. If $ (1 + \alpha)(1 + \gamma) < 1 $ then the degree distribution converges to a stationary distribution, which in most cases has an approximately power law tail with an index which depends on $ \alpha $ and $ \gamma $. If $ (1 + \alpha)(1 + \gamma) > 1 $ then the degree of a typical vertex grows to infinity, and the proportion of vertices having any fixed degree $d$ tends to zero. We also give some results on the number of edges and on the spectral gap.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "reproducing graphs, random graphs, degree distribution, phase transition", } @Article{Hajri:2011:SFR, author = "Hatem Hajri", title = "Stochastic Flows Related to {Walsh Brownian} Motion", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "58:1563--58:1599", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-924", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/924", abstract = "We define an equation on a simple graph which is an extension of Tanaka's equation and the skew Brownian motion equation. We then apply the theory of transition kernels developed by Le Jan and Raimond and show that all the solutions can be classified by probability measures.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic flows of kernels, Skew Brownian motion, Walsh Brownian motion", } @Article{Meerschaert:2011:FPP, author = "Mark Meerschaert and Erkan Nane and P. Vellaisamy", title = "The Fractional {Poisson} Process and the Inverse Stable Subordinator", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "59:1600--59:1620", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-920", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/920", abstract = "The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional diffusion equations. The equivalence extends to a broad class of renewal processes that include models for tempered fractional diffusion, and distributed-order (e.g., ultraslow) fractional diffusion. The paper also {discusses the relation between} the fractional Poisson process and Brownian time.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Caputo fractional derivative; Continuous time random walk limit; Di; Fractional difference-differential equations; Fractional Poisson process; Generalized Mittag-leffler function; Inverse stable subordinator; Mittag-Leffler waiting time; Renewal process", } @Article{Benaych-Georges:2011:FEE, author = "Florent Benaych-Georges and Alice Guionnet and Myl{\`e}ne Maida", title = "Fluctuations of the Extreme Eigenvalues of Finite Rank Deformations of Random Matrices", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "60:1621--60:1662", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-929", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/929", abstract = "Consider a deterministic self-adjoint matrix $ X_n $ with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by adding a random finite rank matrix with delocalised eigenvectors and study the extreme eigenvalues of the deformed model. We give necessary conditions on the deterministic matrix $ X_n $ so that the eigenvalues converging out of the bulk exhibit Gaussian fluctuations, whereas the eigenvalues sticking to the edges are very close to the eigenvalues of the non-perturbed model and fluctuate in the same scale.\par We generalize these results to the case when $ X_n $ is random and get similar behavior when we deform some classical models such as Wigner or Wishart matrices with rather general entries or the so-called matrix models.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "extreme eigenvalue statistics; Gaussian fluctuations; random matrices; spiked models; Tracy--Widom laws", } @Article{Villemonais:2011:IPS, author = "Denis Villemonais", title = "Interacting Particle Systems and {Yaglom} Limit Approximation of Diffusions with Unbounded Drift", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "61:1663--61:1692", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-925", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/925", abstract = "We study the existence and the exponential ergodicity of a general interacting particle system, whose components are driven by independent diffusion processes with values in an open subset of $ \mathbb {R}^d $, $ d \geq 1 $. The interaction occurs when a particle hits the boundary: it jumps to a position chosen with respect to a probability measure depending on the position of the whole system. Then we study the behavior of such a system when the number of particles goes to infinity. This leads us to an approximation method for the Yaglom limit of multi-dimensional diffusion processes with unbounded drift defined on an unbounded open set. While most of known results on such limits are obtained by spectral theory arguments and are concerned with existence and uniqueness problems, our approximation method allows us to get numerical values of quasi-stationary distributions, which find applications to many disciplines. We end the paper with numerical illustrations of our approximation method for stochastic processes related to biological population models.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "diffusion process; empirical process; interacting particle system; quasi-stationary distribution; Yaglom limit", } @Article{Folz:2011:GUB, author = "Matthew Folz", title = "{Gaussian} Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "62:1693--62:1722", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-926", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/926", abstract = "We consider continuous time simple random walks with arbitrary speed measure $ \theta $ on infinite weighted graphs. Write $ p_t(x, y) $ for the heat kernel of this process. Given on-diagonal upper bounds for the heat kernel at two points $ x_1, x_2 $, we obtain a Gaussian upper bound for $ p_t(x_1, x_2) $. The distance function which appears in this estimate is not in general the graph metric, but a new metric which is adapted to the random walk. Long-range non-Gaussian bounds in this new metric are also established. Applications to heat kernel bounds for various models of random walks in random environments are discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian upper bound; heat kernel; random walk; random walk in random environment", } @Article{Dasgupta:2011:SLU, author = "Amites Dasgupta and Krishanu Maulik", title = "Strong Laws for Urn Models with Balanced Replacement Matrices", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "63:1723--63:1749", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-928", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/928", abstract = "We consider an urn model, whose replacement matrix has all entries nonnegative and is balanced, that is, has constant row sums. We obtain the rates of the counts of balls corresponding to each color for the strong laws to hold. The analysis requires a rearrangement of the colors in two steps. We first reduce the replacement matrix to a block upper triangular one, where the diagonal blocks are either irreducible or the scalar zero. The scalings for the color counts are then given inductively depending on the Perron--Frobenius eigenvalues of the irreducible diagonal blocks. In the second step of the rearrangement, the colors are further rearranged to reduce the block upper triangular replacement matrix to a canonical form. Under a further mild technical condition, we obtain the scalings and also identify the limits. We show that the limiting random variables corresponding to the counts of colors within a block are constant multiples of each other. We provide an easy-to-understand explicit formula for them as well. The model considered here contains the urn models with irreducible replacement matrix, as well as, the upper triangular one and several specific block upper triangular ones considered earlier in the literature and gives an exhaustive picture of the color counts in the general case with only possible restrictions that the replacement matrix is balanced and has nonnegative entries.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Urn model, balanced triangular replacement matrix, Perron--Frobenius eigenvalue, irreducible matrix", } @Article{Capitaine:2011:FCS, author = "Mireille Capitaine and Catherine Donati-Martin and Delphine F{\'e}ral and Maxime F{\'e}vrier", title = "Free Convolution with a Semicircular Distribution and Eigenvalues of Spiked Deformations of {Wigner} Matrices", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "64:1750--64:1792", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-934", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/934", abstract = "We investigate the asymptotic spectrum of spiked perturbations of Wigner matrices. The entries of the Wigner matrix have a distribution which is symmetric and satisfies a Poincar{\'e} inequality. The spectral measure of the deterministic Hermitian perturbation matrix converges to some probability measure with compact support. We also assume that this perturbation matrix has a fixed number of fixed eigenvalues (spikes) outside the support of its limiting spectral measure whereas the distance between the other eigenvalues and this support uniformly goes to zero as the dimension goes to infinity. We establish that only a particular subset of the spikes will generate some eigenvalues of the deformed model, which will converge to some limiting points outside the support of the limiting spectral measure. This phenomenon can be fully described in terms of free probability involving the subordination function related to the free additive convolution by a semicircular distribution. Note that only finite rank perturbations had been considered up to now (even in the deformed GUE case).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Asymptotic spectrum; Deformed Wigner matrices; Extreme eigenvalues; Free probability; Random matrices; Stieltjes transform; Subordination property", } @Article{Antunovic:2011:IZB, author = "Tonci Antunovic and Krzysztof Burdzy and Yuval Peres and Julia Ruscher", title = "Isolated Zeros for {Brownian} Motion with Variable Drift", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "65:1793--65:1814", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-927", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/927", abstract = "It is well known that standard one-dimensional Brownian motion $ B(t) $ has no isolated zeros almost surely. We show that for any $ \alpha < 1 / 2 $ there are alpha-H{\"o}lder continuous functions $f$ for which the process $ B - f$ has isolated zeros with positive probability. We also prove that for any continuous function $f$, the zero set of $ B - f$ has Hausdorff dimension at least $ 1 / 2$ with positive probability, and $ 1 / 2$ is an upper bound on the Hausdorff dimension if $f$ is $ 1 / 2$-H{\"o}lder continuous or of bounded variation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; Cantor function; Hausdorff dimension; H{\"o}lder continuity; isolated zeros", } @Article{Benaim:2011:SID, author = "Michel Bena{\"\i}m and Olivier Raimond", title = "Self-Interacting Diffusions {IV}: Rate of Convergence", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "66:1815--66:1843", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-948", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/948", abstract = "Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is governed by a deterministic dynamical system and under certain conditions it converges almost surely towards a deterministic measure. (see Bena{\"\i}m, Ledoux, Raimond (2002) and Bena{\"\i}m, Raimond (2005)). We are interested here in the rate of this convergence. A central limit theorem is proved. In particular, this shows that greater is the interaction repelling faster is the convergence.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Self-interacting random processes, reinforced processes", } @Article{Soner:2011:QSS, author = "Mete Soner and Nizar Touzi and Jianfeng Zhang", title = "Quasi-sure Stochastic Analysis through Aggregation", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "67:1844--67:1879", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-950", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/950", abstract = "This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic representations of fully nonlinear partial differential equations and applications to mathematical finance. The existing literature relies either on the capacity theory (Denis and Martini), or on the underlying nonlinear partial differential equation (Peng). In both approaches, the resulting theory requires certain smoothness, the so-called quasi-sure continuity, of the corresponding processes and random variables in terms of the underlying canonical process. In this paper, we investigate this question for a larger class of ``non-smooth'' processes, but with a restricted family of non-dominated probability measures. For smooth processes, our approach leads to similar results as in previous literature, provided the restricted family satisfies an additional density property.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "non-dominated probability measures, weak solutions of SDEs, uncertain volatility model, quasi-sure stochastic analysis", } @Article{Friz:2011:NHD, author = "Peter Friz and Nicolas Victoir", title = "A Note on Higher Dimensional $p$-Variation", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "68:1880--68:1899", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-951", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/951", abstract = "We discuss $p$-variation regularity of real-valued functions defined on $ [0, T] \times [0, T]$, based on rectangular increments. When $ p > 1$, there are two slightly different notions of $p$-variation; both of which are useful in the context of Gaussian rough paths. Unfortunately, these concepts were blurred in previous works; the purpose of this note is to show that the aforementioned notions of $p$-variations are ``epsilon-close''. In particular, all arguments relevant for Gaussian rough paths go through with minor notational changes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "higher dimensional p-variation, Gaussian rough paths", } @Article{Bansaye:2011:ULD, author = "Vincent Bansaye and Christian B{\"o}inghoff", title = "Upper large deviations for Branching Processes in Random Environment with heavy tails", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "69:1900--69:1933", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-933", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/933", abstract = "Branching Processes in Random Environment (BPREs) $ (Z_n \colon n \geq 0) $ are the generalization of Galton--Watson processes where \lq in each generation' the reproduction law is picked randomly in an i.i.d. manner. The associated random walk of the environment has increments distributed like the logarithmic mean of the offspring distributions. This random walk plays a key role in the asymptotic behavior. In this paper, we study the upper large deviations of the BPRE $Z$ when the reproduction law may have heavy tails. More precisely, we obtain an expression for the limit of $ - \log \mathbb {P}(Z_n \geq \exp (\theta n)) / n$ when $ n \rightarrow \infty $. It depends on the rate function of the associated random walk of the environment, the logarithmic cost of survival $ \gamma := - \lim_{n \rightarrow \infty } \log \mathbb {P}(Z_n > 0) / n$ and the polynomial rate of decay $ \beta $ of the tail distribution of $ Z_1$. This rate function can be interpreted as the optimal way to reach a given ``large'' value. We then compute the rate function when the reproduction law does not have heavy tails. Our results generalize the results of B{\"o}inghoff $ \& a m p; $ Kersting (2009) and Bansaye $ \& a m p; $ Berestycki (2008) for upper large deviations. Finally, we derive the upper large deviations for the Galton--Watson processes with heavy tails.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching processes, random environment, large deviations, random walks, heavy tails", } @Article{Loubaton:2011:ASL, author = "Philippe Loubaton and Pascal Vallet", title = "Almost Sure Localization of the Eigenvalues in a {Gaussian} Information Plus Noise Model. {Application} to the Spiked Models", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "70:1934--70:1959", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-943", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/943", abstract = "Let $S$ be a $M$ times $N$ random matrix defined by $ S = B + \sigma W$ where $B$ is a uniformly bounded deterministic matrix and where $W$ is an independent identically distributed complex Gaussian matrix with zero mean and variance $ 1 / N$ entries. The purpose of this paper is to study the almost sure location of the eigenvalues of the Gram matrix $ S S^*$ when $M$ and $N$ converge to infinity such that the ratio $ M / N$ converges towards a constant $ c > 0$. The results are used in order to derive, using an alternative approach, known results concerning the behavior of the largest eigenvalues of $ S S^*$ when the rank of $B$ remains fixed and $M$ and $N$ converge to infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "gaussian information plus noise model; localization of the eigenvalues; random matrix theory; spiked models", } @Article{Uchiyama:2011:FHT, author = "Kohei Uchiyama", title = "The First Hitting Time of a Single Point for Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "71:1960--71:2000", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-931", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/931", abstract = "This paper concerns the first hitting time $ T_0 $ of the origin for random walks on $d$-dimensional integer lattice with zero mean and a finite $ 2 + \delta $ absolute moment ($ \delta \geq 0$). We derive detailed asymptotic estimates of the probabilities $ \mathbb {P}_x(T_0 = n)$ as $ n \to \infty $ that are valid uniformly in $x$, the position at which the random walks start.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "asymptotic expansion; Fourier analysis; hitting time; random walk", } @Article{Devroye:2011:NPC, author = "Luc Devroye", title = "A Note on the Probability of Cutting a {Galton--Watson} Tree", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "72:2001--72:2019", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-952", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/952", abstract = "The structure of Galton--Watson trees conditioned to be of a given size is well-understood. We provide yet another embedding theorem that permits us to obtain asymptotic probabilities of events that are determined by what happens near the root of these trees. As an example, we derive the probability that a Galton--Watson tree is cut when each node is independently removed with probability p, where by cutting a tree we mean that every path from root to leaf must have at least one removed node.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Galton--Watson tree; probabilistic analysis of algorithms, branching process", } @Article{Barczy:2011:FLT, author = "Matyas Barczy and Jean Bertoin", title = "Functional Limit Theorems for {L{\'e}vy} Processes Satisfying {Cram{\'e}r}'s Condition", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "73:2020--73:2038", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-930", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/930", abstract = "We consider a L{\'e}vy process that starts from $ x < 0 $ and conditioned on having a positive maximum. When Cram{\'e}r's condition holds, we provide two weak limit theorems as $x$ goes to $ - \infty $ for the law of the (two-sided) path shifted at the first instant when it enters $ (0, \infty)$, respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cram{\'e}r's condition; L{\'e}vy process; self-similar Markov process", } @Article{Chakrabarty:2011:ANH, author = "Arijit Chakrabarty", title = "Asymptotic Normality of Hill Estimator for Truncated Data", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "74:2039--74:2058", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-935", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/935", abstract = "The problem of estimating the tail index from truncated data is addressed in [2]. In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untruncated situation, asymptotic normality of the Hill estimator is well known for distributions whose tail belongs to the Hall class, see [11]. Motivated by this, we show the same in the truncated case for that class.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "heavy tails, truncation, second order regular variation, Hill estimator, asymptotic normality", } @Article{Bojdecki:2011:NVH, author = "Tomasz Bojdecki and Luis Gorostiza and Anna Talarczyk", title = "Number Variance for Hierarchical Random Walks and Related Fluctuations", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "75:2059--75:2079", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-937", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/937", abstract = "We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the $c$-random walks. Such walks are used, e.g., in mathematical physics and population biology. The number variance problem consists in investigating if the variance of the number of `particles' $ N_n(L) $ lying in the ball of radius $L$ at a given step $n$ remains bounded, or even better, converges to a finite limit, as $ L \to \infty $. We give a necessary and sufficient condition and discuss its relationship to transience/recurrence property of the walk. Next we consider normalized fluctuations of $ N_n(L)$ around the mean as $ n \to \infty $ and $L$ is increased in an appropriate way. We prove convergence of finite dimensional distributions to a Gaussian process whose properties are discussed. As the $c$-random walks mimic symmetric stable processes on $ \mathbb {R}$, we compare our results with those obtained by Hambly and Jones (2007, 2009), who studied the number variance problem for an infinite system of independent symmetric stable processes on $ \mathbb {R}$. Since the hierarchical group is an ultrametric space, corresponding results for symmetric stable processes and hierarchical random walks may be analogous or quite different, as has been observed in other contexts. An example of a difference in the present context is that for the stable processes a fluctuation limit process is a Gaussian process which is not Markovian and has long range dependent stationary increments, but the counterpart for hierarchical random walks is Markovian, and in a special case it has independent increments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fluctuation; hierarchical group; hierarchical random walk; limit theorem; number variance; ultrametric", } @Article{Tribe:2011:PFO, author = "Roger Tribe and Oleg Zaboronski", title = "{Pfaffian} Formulae for One Dimensional Coalescing and Annihilating Systems", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "76:2080--76:2103", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-942", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/942", abstract = "The paper considers instantly coalescing, or instantly annihilating, systems of one-dimensional Brownian particles on the real line. Under maximal entrance laws, the distribution of the particles at a fixed time is shown to be Pfaffian point processes closely related to the Pfaffian point process describing one dimensional distribution of real eigenvalues in the real Ginibre ensemble of random matrices. As an application, an exact large time asymptotic for the $n$-point density function for coalescing particles is derived.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "annihilating/coalescing Brownian motions, real Ginibre ensemble, random matrices, Pfaffian point processes", } @Article{Tao:2011:WDM, author = "Terence Tao and Van Vu", title = "The {Wigner--Dyson--Mehta} Bulk Universality Conjecture for {Wigner} Matrices", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "77:2104--77:2121", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-944", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/944", abstract = "A well known conjecture of Wigner, Dyson, and Mehta asserts that the (appropriately normalized) $k$-point correlation functions of the eigenvalues of random $ n \times n$ Wigner matrices in the bulk of the spectrum converge (in various senses) to the $k$-point correlation function of the Dyson sine process in the asymptotic limit $ n \to \infty $. There has been much recent progress on this conjecture; in particular, it has been established under a wide variety of decay, regularity, and moment hypotheses on the underlying atom distribution of the Wigner ensemble, and using various notions of convergence. Building upon these previous results, we establish new instances of this conjecture with weaker hypotheses on the atom distribution and stronger notions of convergence. In particular, assuming only a finite moment condition on the atom distribution, we can obtain convergence in the vague sense, and assuming an additional regularity condition, we can upgrade this convergence to locally $ L^1$ convergence. As an application, we determine the limiting distribution of the number of eigenvalues $ N_I$ in a short interval $I$ of length $ \Theta (1 / n)$. As a corollary of this result, we obtain an extension of a result of Jimbo et. al. concerning the behavior of spacing in the bulk.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random matrices; universality", } @Article{Etheridge:2011:DAM, author = "Alison Etheridge and Sophie Lemaire", title = "Diffusion Approximation of a Multilocus Model with Assortative Mating", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "78:2122--78:2181", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-932", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/932", abstract = "To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population evolves according to a Moran model with weak assortative mating, strong recombination and low mutation rates. With an appropriate rescaling of time, we obtain that the evolution of the genotypic frequencies in a large population can be approximated by the evolution of the product of the allelic frequencies at each locus, and the vector of the allelic frequencies is approximately governed by a diffusion. The same diffusion limit can be obtained for a multilocus model of a diploid population subject to selection. We present some features of the limiting diffusions (in particular their boundary behaviour and conditions under which the allelic frequencies at different loci evolve independently). If mutation rates are strictly positive then the limiting diffusion is reversible and, under some assumptions, the critical points of the stationary density can be characterised.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "assortative mating; diffusion approximation; diploid selection; Moran model; multilocus models; population genetics", } @Article{Griffin:2011:TWL, author = "Philip Griffin and Ross Maller", title = "The Time at which a {L{\'e}vy} Process Creeps", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "79:2182--79:2202", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-945", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/945", abstract = "We show that if a Levy process creeps then the renewal function of the bivariate ascending ladder process satisfies certain continuity and differentiability properties. Then a left derivative of the renewal function is shown to be proportional to the distribution function of the time at which the process creeps over a given level, where the constant of proportionality is the reciprocal of the (positive) drift of the ascending ladder height process. This allows us to add the term due to creeping in the recent quintuple law of Doney and Kyprianou (2006). As an application, we derive a Laplace transform identity which generalises the second factorization identity. We also relate Doney and Kyprianou's extension of Vigon's equation amicale inverse to creeping. Some results concerning the ladder process, including the second factorization identity, continue to hold for a general bivariate subordinator, and are given in this generality.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "L{\'e}vy process, quintuple law, creeping by time $t$, second factorization identity, bivariate subordinator", } @Article{Janson:2011:TEL, author = "Svante Janson and G{\"o}tz Kersting", title = "On the Total External Length of the {Kingman} Coalescent", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "80:2203--80:2218", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-955", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/955", abstract = "We prove asymptotic normality of the total length of external branches in the Kingman coalescent. The proof uses an embedded Markov chain, which can be described as follows: Take an urn with black balls. Empty it step by step according to the rule: In each step remove a randomly chosen pair of balls and replace it by one red ball. Finally remove the last remaining ball. Then the numbers of red balls form a Markov chain with an unexpected property: It is time-reversible.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coalescent, external branch, reversibility, urn model", } @Article{ORourke:2011:PIN, author = "Sean O'Rourke and Alexander Soshnikov", title = "Products of Independent non-{Hermitian} Random Matrices", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "81:2219--81:2245", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-954", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/954", abstract = "We consider the product of a finite number of non-Hermitian random matrices with i.i.d. centered entries of growing size. We assume that the entries have a finite moment of order bigger than two. We show that the empirical spectral distribution of the properly normalized product converges, almost surely, to a non-random, rotationally invariant distribution with compact support in the complex plane. The limiting distribution is a power of the circular law.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Circular law; Random matrices", } @Article{Petrov:2011:PSD, author = "Leonid Petrov", title = "{Pfaffian} Stochastic Dynamics of Strict Partitions", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "82:2246--82:2295", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-956", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/956", abstract = "We study a family of continuous time Markov jump processes on strict partitions (partitions with distinct parts) preserving the distributions introduced by Borodin (1997) in connection with projective representations of the infinite symmetric group. The one-dimensional distributions of the processes (i.e., the Borodin's measures) have determinantal structure. We express the dynamical correlation functions of the processes in terms of certain Pfaffians and give explicit formulas for both the static and dynamical correlation kernels using the Gauss hypergeometric function. Moreover, we are able to express our correlation kernels (both static and dynamical) through those of the z-measures on partitions obtained previously by Borodin and Olshanski in a series of papers. The results about the fixed time case were announced in the note [El. Comm. Probab., 15 (2010), 162-175]. A part of the present paper contains proofs of those results.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "determinantal point process; Pfaffian dynamics; random strict partitions", } @Article{Boissard:2011:SBC, author = "Emmanuel Boissard", title = "Simple Bounds for the Convergence of Empirical and Occupation Measures in $1$-{Wasserstein} Distance", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "83:2296--83:2333", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-958", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/958", abstract = "We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the reference measure satisfies a transport-entropy inequality. We extend some results of F. Bolley, A. Guillin and C. Villani with simple proofs. Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a contracting Markov chain in 1-Wasserstein distance are also given. Throughout the text, several examples are worked out, including the cases of Gaussian measures on separable Banach spaces, and laws of diffusion processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Uniform deviations, Transport inequalities", } @Article{Groeneboom:2011:VLC, author = "Piet Groeneboom", title = "Vertices of the Least Concave Majorant of {Brownian} Motion with Parabolic Drift", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "84:2334--84:2358", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-959", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See erratum \cite{Groeneboom:2013:EVL}.", URL = "http://ejp.ejpecp.org/article/view/959", abstract = "It was shown in Groeneboom (1983) that the least concave majorant of one-sided Brownian motion without drift can be characterized by a jump process with independent increments, which is the inverse of the process of slopes of the least concave majorant. This result can be used to prove the result in Sparre Andersen (1954) that the number of vertices of the smallest concave majorant of the empirical distribution function of a sample of size $n$ from the uniform distribution on $ [0, 1]$ is asymptotically normal, with an asymptotic expectation and variance which are both of order $ \log (n)$. A similar (Markovian) inverse jump process was introduced in Groeneboom (1989), in an analysis of the least concave majorant of two-sided Brownian motion with a parabolic drift. This process is quite different from the process for one-sided Brownian motion without drift: the number of vertices in a (corresponding slopes) interval has an expectation proportional to the length of the interval and the variance of the number of vertices in such an interval is about half the size of the expectation, if the length of the interval tends to infinity. We prove an asymptotic normality result for the number of vertices in an increasing interval, which translates into a corresponding result for the least concave majorant of an empirical distribution function of a sample of size $n$, generated by a strictly concave distribution function. In this case the number of vertices is of order cube root $n$ and the variance is again about half the size of the asymptotic expectation. As a side result we obtain some interesting relations between the first moments of the number of vertices, the square of the location of the maximum of Brownian motion minus a parabola, the value of the maximum itself, the squared slope of the least concave majorant at zero, and the value of the least concave majorant at zero.\par An erratum is available in {\bf \url{https://doi.org/10.1214/EJP.v18-2697} EJP volume {\bf 18} paper 46}.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, parabolic drift, number of vertices, concave majorant, Airy functions, jump processes, Grenander estimator", } @Article{Sapatinas:2011:SNA, author = "Theofanis Sapatinas and Damodar Shanbhag and Arjun Gupta", title = "Some New Approaches to Infinite Divisibility", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "85:2359--85:2374", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-961", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/961", abstract = "Using an approach based, amongst other things, on Proposition 1 of Kaluza (1928), Goldie (1967) and, using a different approach based especially on zeros of polynomials, Steutel (1967) have proved that each nondegenerate distribution function (d.f.) $F$ (on $ \mathbb {R}$, the real line), satisfying $ F(0 -) = 0$ and $ F(x) = F(0) + (1 - F(0))G(x), x > 0$, where $G$ is the d.f. corresponding to a mixture of exponential distributions, is infinitely divisible. Indeed, Proposition 1 of Kaluza (1928) implies that any nondegenerate discrete probability distribution $ \{ p_x \colon x = 0, 1, \ldots \} $ that is log-convex or, in particular, completely monotone, is compound geometric, and, hence, infinitely divisible. Steutel (1970), Shanbhag \& Sreehari (1977) and Steutel \& van Harn (2004, Chapter VI) have given certain extensions or variations of one or more of these results. Following a modified version of the C. R. Rao {\em et al.} (2009, Section 4) approach based on the Wiener--Hopf factorization, we establish some further results of significance to the literature on infinite divisibility.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Infinite divisibility; Kaluza sequences; Log-convexity; Mixtures of exponential distributions; Mixtures of geometric distributions; Wiener--Hopf factorization", } @Article{Dobler:2011:SMM, author = "Christian D{\"o}bler and Michael Stolz", title = "{Stein}'s Method and the Multivariate {CLT} for Traces of Powers on the Compact Classical Groups", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "86:2375--86:2405", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-960", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/960", abstract = "Let $M$ be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed according to Haar measure. By a classical result of Diaconis and Shahshahani, for large matrix size $n$, the vector of traces of consecutive powers of $M$ tends to a vector of independent (real or complex) Gaussian random variables. Recently, Jason Fulman has demonstrated that for a single power $j$ (which may grow with $n$), a speed of convergence result may be obtained via Stein's method of exchangeable pairs. In this note, we extend Fulman's result to the multivariate central limit theorem for the full vector of traces of powers.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random matrices, compact Lie groups, Haar measure, traces of powers, Stein's method, normal approximation, exchangeable pairs, heat kernel, power sum symmetric polynomials", } @Article{Matic:2011:LDP, author = "Ivan Matic", title = "Large Deviations for Processes in Random Environments with Jumps", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "87:2406--87:2438", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-962", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/962", abstract = "A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We study the exponential decay of the probabilities that the walk will reach sites located far away from the origin. We also study a similar problem for the continuous analogue: the process that is a solution to an ODE with random coefficients. In this second model the environment also has ``teleports'' which are the regions from where the process can make discontinuous jumps.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "deterministic walks in random environments.; large deviations; processes in random environments", } @Article{Bai:2011:NRC, author = "Zhidong Bai and Jiang Hu and Guangming Pan and Wang Zhou", title = "A Note on Rate of Convergence in Probability to Semicircular Law", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "88:2439--88:2451", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-963", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/963", abstract = "In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is $ O(n^{-1 / 2}) $ when the dimension n tends to infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "convergence rate, Wigner matrix, Semicircular Law, spectral distribution", } @Article{Louhichi:2011:FCS, author = "Sana Louhichi and Emmanuel Rio", title = "Functional Convergence to Stable {L{\'e}vy} Motions for Iterated Random {Lipschitz} Mappings", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "89:2452--89:2480", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-965", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/965", abstract = "It is known that, in the dependent case, partial sums processes which are elements of $ D([0, 1]) $ (the space of right-continuous functions on $ [0, 1] $ with left limits) do not always converge weakly in the $ J_1$-topology sense. The purpose of our paper is to study this convergence in $ D([0, 1])$ equipped with the $ M_1$-topology, which is weaker than the $ J_1$ one. We prove that if the jumps of the partial sum process are associated then a functional limit theorem holds in $ D([0, 1])$ equipped with the $ M_1$-topology, as soon as the convergence of the finite-dimensional distributions holds. We apply our result to some stochastically monotone Markov chains arising from the family of iterated Lipschitz models.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Partial sums processes. Skorohod topologies. Functional limit theorem. Association. Tightness. Ottaviani inequality. Stochastically monotone Markov chains. Iterated random Lipschitz mappings", } @Article{Devroye:2011:HDR, author = "Luc Devroye and Andr{\'a}s Gy{\"o}rgy and G{\'a}bor Lugosi and Frederic Udina", title = "High-Dimensional Random Geometric Graphs and their Clique Number", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "90:2481--90:2508", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-967", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/967", abstract = "We study the behavior of random geometric graphs in high dimensions. We show that as the dimension grows, the graph becomes similar to an Erd{\H{o}}s--R{\'e}nyi random graph. We pay particular attention to the clique number of such graphs and show that it is very close to that of the corresponding Erd{\H{o}}s--R{\'e}nyi graph when the dimension is larger than $ \log^3 (n) $ where $n$ is the number of vertices. The problem is motivated by a statistical problem of testing dependencies.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Clique number; dependency testing; geometric graphs; random graphs", } @Article{Penrose:2011:LCL, author = "Mathew Penrose and Yuval Peres", title = "Local {Central Limit Theorems} in Stochastic Geometry", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "91:2509--91:2544", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-968", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/968", abstract = "We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply this result to various quantities arising in stochastic geometry, including: size of the largest component for percolation on a box; number of components, number of edges, or number of isolated points, for random geometric graphs; covered volume for germ-grain coverage models; number of accepted points for finite-input random sequential adsorption; sum of nearest-neighbour distances for a random sample from a continuous multidimensional distribution.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Local central limit theorem; nearest neighbours; percolation; random geometric graph; stochastic geometry", } @Article{Liitiainen:2011:AMN, author = "Elia Liiti{\"a}inen", title = "Asymptotic Moments of Near Neighbor Distances for the {Gaussian} Distribution", journal = j-ELECTRON-J-PROBAB, volume = "16", pages = "92:2545--92:2573", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v16-969", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/969", abstract = "We study the moments of the k-th nearest neighbor distance for independent identically distributed points in $ \mathbb {R}^n $. In the earlier literature, the case with power higher than n has been analyzed by assuming a bounded support for the underlying density. The boundedness assumption is removed by assuming the multivariate Gaussian distribution. In this case, the nearest neighbor distances show very different behavior in comparison to earlier results.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "gaussian; moments; nearest neighbor; random geometry", } @Article{Evans:2012:TPT, author = "Steven Evans and Rudolf Gr{\"u}bel and Anton Wakolbinger", title = "Trickle-down processes and their boundaries", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "1:1--1:58", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1698", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1698", abstract = "It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in one-by-one at a distinguished source vertex, successive particles proceed along directed edges according to an appropriate stochastic mechanism, and each particle comes to rest once it encounters an unoccupied vertex. Examples include the binary and digital search tree processes, the random recursive tree process and generalizations of it arising from nested instances of Pitman's two-parameter Chinese restaurant process, tree-growth models associated with Mallows' $ \phi $ model of random permutations and with Sch{\"u}tzenberger's non-commutative $q$-binomial theorem, and a construction due to Luczak and Winkler that grows uniform random binary trees in a Markovian manner. We introduce a framework that encompasses such Markov chains, and we characterize their asymptotic behavior by analyzing in detail their Doob--Martin compactifications, Poisson boundaries and tail $ \sigma $-fields.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Catalan; Chinese restaurant process; diffusion limited aggregation; Dirichlet random measure; Ewens sampling formula; GEM distribution; h-transform; harmonic function; Mallows model; q-binomial; random recursive tree; search tree; tail sigma-field", } @Article{denHollander:2012:MKD, author = "Frank den Hollander and Francesca Nardi and Alessio Troiani", title = "Metastability for {Kawasaki} dynamics at low temperature with two types of particles", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "2:1--2:26", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1693", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1693", abstract = "This is the first in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics at low temperature in a large finite box with an open boundary. Each pair of particles occupying neighboring sites has a negative binding energy provided their types are different, while each particle has a positive activation energy that depends on its type. There is no binding energy between neighboring particles of the same type. At the boundary of the box particles are created and annihilated in a way that represents the presence of an infinite gas reservoir. We start the dynamics from the empty box and compute the transition time to the full box. This transition is triggered by a critical droplet appearing somewhere in the box. We identify the region of parameters for which the system is metastable. For this region, in the limit as the temperature tends to zero, we show that the first entrance distribution on the set of critical droplets is uniform, compute the expected transition time up to a multiplicative factor that tends to one, and prove that the transition time divided by its expectation is exponentially distributed. These results are derived under three hypotheses on the energy landscape, which are verified in the second and the third paper for a certain subregion of the metastable region. These hypotheses involve three model-dependent quantities - the energy, the shape and the number of the critical droplets - which are identified in the second and the third paper as well.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "capacity; critical droplet; Dirichlet form; Kawasaki dynamics; metastable region; metastable transition time; Multi-type particle systems; potential theory", } @Article{Croydon:2012:CMT, author = "David Croydon and Ben Hambly and Takashi Kumagai", title = "Convergence of mixing times for sequences of random walks on finite graphs", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "3:1--3:32", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1705", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1705", abstract = "We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a suitable Gromov--Hausdorff sense. With this result we are able to establish the convergence of the mixing times on the largest component of the Erd{\H{o}}s--R{\'e}nyi random graph in the critical window, sharpening previous results for this random graph model. Our results also enable us to establish convergence in a number of other examples, such as finitely ramified fractal graphs, Galton--Watson trees and the range of a high-dimensional random walk.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractal graph; Galton--Watson tree; Gromov--Hausdorff convergence; mixing; random graph; random walk", } @Article{Denisov:2012:ORW, author = "Denis Denisov and Vitali Wachtel", title = "Ordered random walks with heavy tails", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "4:1--4:21", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1719", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1719", abstract = "This note continues paper of Denisov and Wachtel (2010), where we have constructed a $k$-dimensional random walk conditioned to stay in the Weyl chamber of type $A$. The construction was done under the assumption that the original random walk has $ k - 1$ moments. In this note we continue the study of killed random walks in the Weyl chamber, and assume that the tail of increments is regularly varying of index $ \alpha < k - 1$. It appears that the asymptotic behaviour of random walks is different in this case. We determine the asymptotic behaviour of the exit time, and, using this information, construct a conditioned process which lives on a partial compactification of the Weyl chamber.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Doob $h$-transform; Dyson's Brownian Motion; Martin boundary; superharmonic function; Weyl chamber", } @Article{Holmgren:2012:NCS, author = "Cecilia Holmgren", title = "Novel characteristics of split trees by use of renewal theory", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "5:1--5:27", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1723", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1723", abstract = "We investigate characteristics of random split trees introduced by Devroye [SIAM J Comput 28, 409-432, 1998]; split trees include e.g., binary search trees, $m$-ary search trees, quadtrees, median of $ (2 k + 1)$-trees, simplex trees, tries and digital search trees. More precisely: We use renewal theory in the studies of split trees, and use this theory to prove several results about split trees. A split tree of cardinality n is constructed by distributing n balls (which often represent data) to a subset of nodes of an infinite tree. One of our main results is a relation between the deterministic number of balls n and the random number of nodes N. In Devroye [SIAM J Comput 28, 409-432, 1998] there is a central limit law for the depth of the last inserted ball so that most nodes are close to depth $ \ln n / \mu + O(\ln n)^{1 / 2})$, where $ \mu $ is some constant depending on the type of split tree; we sharpen this result by finding an upper bound for the expected number of nodes with depths $ \geq \mu^{-1} \ln n - (\ln n)^{1 / 2 + \epsilon }$ or depths $ \leq \mu^{-1} \ln n + (\ln n)^{1 / 2 + \epsilon }$ for any choice of $ \epsilon > 0$. We also find the first asymptotic of the variances of the depths of the balls in the tree.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random Trees, Split Trees, Renewal Theory", } @Article{DeMasi:2012:TCS, author = "Anna {De Masi} and Errico Presutti and Dimitrios Tsagkarogiannis and Maria Vares", title = "Truncated correlations in the stirring process with births and deaths", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "6:1--6:35", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1734", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1734", abstract = "We consider the stirring process in the interval $ \Lambda_N := [ - N, N] $ of $ \mathbb Z $ with births and deaths taking place in the intervals $ I_+ := (N - K, N] $, and respectively $ I_- := [ - N, - N + K) $, $ 1 \leq K < N $. We prove bounds on the truncated moments uniform in $N$ which yield strong factorization properties.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "hydrodynamic limits; nonlinear boundary processes.; stirring process; truncated correlations; v-functions", } @Article{Marcus:2012:CLT, author = "Michael Marcus and Jay Rosen", title = "Central limit theorems for the {$ L^2 $} norm of increments of local times of {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "7:1--7:111", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1740", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1740", abstract = "Let $ X = \{ X_t, t \in R_+ \} $ be a symmetric L{\'e}vy process with local time $ \{ L^{ x }_{ t} \,; \, (x, t) \in R^{ 1} \times R^{ 1}_{ +} \} $. When the L{\'e}vy exponent $ \psi (\lambda) $ is regularly varying at zero with index $ 1 < \beta \leq 2 $, and satisfies some additional regularity conditions,\par $$ \lim_{t \to \infty }{ \int_{- \infty }^{\infty } (L^{ x + 1}_t - L^{ x}_{ t})^{ 2} \, dx - E \left (\int_{- \infty }^{\infty } (L^{ x + 1}_t - L^{ x}_{ t})^{ 2} \, dx \right) \over t \sqrt {\psi^{-1}(1 / t)}} $$ is equal in law to\par $$ (8 c_{\psi, 1 })^{1 / 2} \left (\int_{- \infty }^{\infty } \left (L_{\beta, 1}^x \right)^2 \, d x \right)^{1 / 2} \, \eta $$ where $ L_{\beta, 1} = \{ L^{ x }_{\beta, 1} \,; \, x \in R^{ 1} \} $ denotes the local time, at time 1, of a symmetric stable process with index $ \beta $, $ \eta $ is a normal random variable with mean zero and variance one that is independent of $ L_{ \beta, 1} $, and $ c_{\psi, 1} $ is a known constant that depends on $ \psi $.\par When the L{\'e}vy exponent $ \psi (\lambda) $ is regularly varying at infinity with index $ 1 < \beta \leq 2 $ and satisfies some additional regularity conditions\par $$ \lim_{h \to 0} \sqrt {h \psi^2(1 / h)} \left \{ \int_{- \infty }^{\infty } (L^{ x + h}_1 - L^{ x}_{ 1})^{ 2} \, d x - E \left (\int_{- \infty }^{\infty } (L^{ x + h}_1 - L^{ x}_{ 1})^{ 2} \, d x \right) \right \} $$ is equal in law to\par $$ (8 c_{\beta, 1})^{1 / 2} \, \, \eta \, \, \left (\int_{- \infty }^{\infty } (L_1^x)^2 \, d x \right)^{1 / 2} $$ where $ \eta $ is a normal random variable with mean zero and variance one that is independent of $ \{ L^{ x }_{ 1}, x \in R^1 \} $, and $ c_{\beta, 1} $ is a known constant.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central Limit Theorem, $L^2$ norm of increments, local time, L{\'e}vy process", } @Article{Kuznetsov:2012:DPE, author = "Alexey Kuznetsov and Juan Carlos Pardo and Mladen Savov", title = "Distributional properties of exponential functionals of {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "8:1--8:35", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1755", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1755", abstract = "We study the distribution of the exponential functional $ I(\xi, \eta) = \int_0^{\infty } \exp (\xi_{t-}) d \eta_t $, where $ \xi $ and $ \eta $ are independent L{\'e}vy processes. In the general setting, using the theory of Markov processes and Schwartz distributions, we prove that the law of this exponential functional satisfies an integral equation, which generalizes Proposition 2.1 in \cite{CPY}. In the special case when $ \eta $ is a Brownian motion with drift, we show that this integral equation leads to an important functional equation for the Mellin transform of $ I(\xi, \eta) $, which proves to be a very useful tool for studying the distributional properties of this random variable. For general L{\'e}vy process $ \xi $ ($ \eta $ being Brownian motion with drift) we prove that the exponential functional has a smooth density on $ \mathbb {R} \setminus \{ 0 \} $, but surprisingly the second derivative at zero may fail to exist. Under the additional assumption that $ \xi $ has some positive exponential moments we establish an asymptotic behaviour of $ \mathbb {P}(I(\xi, \eta) > x) $ as $ x \to + \infty $, and under similar assumptions on the negative exponential moments of $ \xi $ we obtain a precise asymptotic expansion of the density of $ I(\xi, \eta) $ as $ x \to 0 $. Under further assumptions on the L{\'e}vy process $ \xi $ one is able to prove much stronger results about the density of the exponential functional and we illustrate some of the ideas and techniques for the case when $ \xi $ has hyper-exponential jumps.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "L{\'e}vy processes, exponential functional, integral equations, Mellin transform, asymptotic expansions", } @Article{Berti:2012:LTE, author = "Patrizia Berti and Luca Pratelli and Pietro Rigo", title = "Limit theorems for empirical processes based on dependent data", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "9:1--9:18", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1765", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1765", abstract = "Let $ (X_n) $ be any sequence of random variables adapted to a filtration $ (\mathcal {G}_n) $. Define $ a_n(\cdot) = P \bigl (X_{n + 1} \in \cdot \mid \mathcal {G}_n \bigr) $, $ b_n = \frac {1}{n} \sum_{i = 0}^{n - 1}a_i $, and $ \mu_n = \frac {1}{n} \, \sum_{i = 1}^n \delta_{X_i} $. Convergence in distribution of the empirical processes\par $$ B_n = \sqrt {n} \, (\mu_n - b_n) \quad \text {and} \quad C_n = \sqrt {n} \, (\mu_n - a_n) $$ is investigated under uniform distance. If $ (X_n) $ is conditionally identically distributed, convergence of $ B_n $ and $ C_n $ is studied according to Meyer--Zheng as well. Some CLTs, both uniform and non uniform, are proved. In addition, various examples and a characterization of conditionally identically distributed sequences are given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "conditional identity in distribution; empirical process; exchangeability; predictive measure; stable convergence", } @Article{Barbu:2012:LSS, author = "Viorel Barbu and Michael Roeckner", title = "Localization of solutions to stochastic porous media equations: finite speed of propagation", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "10:1--10:11", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1768", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1768", abstract = "It is proved that the solutions to the slow diffusion stochastic porous media equation $ d X - {\Delta }(|X|^{m - 1}X)d t = \sigma (X)d W_t, $ $ 1 < m \leq 5, $ in $ \mathcal {O} \subset \mathbb {R}^d, \ d = 1, 2, 3, $ have the property of finite speed of propagation of disturbances for $ \mathbb {P} \text {-a.s.} $ $ {\omega } \in {\Omega } $ on a sufficiently small time interval $ (0, t({\omega })) $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "energy method; porous media equation; stochastic flow; Wiener process", } @Article{Bieniek:2012:EFV, author = "Mariusz Bieniek and Krzysztof Burdzy and Soumik Pal", title = "Extinction of {Fleming--Viot}-type particle systems with strong drift", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "11:1--11:15", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1770", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1770", abstract = "We consider a Fleming--Viot-type particle system consisting of independently moving particles that are killed on the boundary of a domain. At the time of death of a particle, another particle branches. If there are only two particles and the underlying motion is a Bessel process on $ (0, \infty) $, both particles converge to 0 at a finite time if and only if the dimension of the Bessel process is less than 0. If the underlying diffusion is Brownian motion with a drift stronger than (but arbitrarily close to, in a suitable sense) the drift of a Bessel process, all particles converge to 0 at a finite time, for any number of particles.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "extinction; Fleming--Viot particle system", } @Article{Rossignol:2012:GPF, author = "Rapha{\"e}l Rossignol and Leandro Pimentel", title = "Greedy polyominoes and first-passage times on random {Voronoi} tilings", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "12:1--12:31", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1788", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1788", abstract = "Let $ \mathcal {N} $ be distributed as a Poisson random set on $ \mathbb {R}^d $, $ d \geq 2 $, with intensity comparable to the Lebesgue measure. Consider the Voronoi tiling of $ \mathbb {R}^d $, $ \{ C_v \}_{v \in \mathcal {N}} $, where $ C_v $ is composed of points $ \mathbf {x} \in \mathbb {R}^d $ that are closer to $ v \in \mathcal {N} $ than to any other $ v' \in \mathcal {N} $. A polyomino $ \mathcal {P} $ of size $n$ is a connected union (in the usual $ \mathbb {R}^d$ topological sense) of $n$ tiles, and we denote by $ \Pi_n$ the collection of all polyominos $ \mathcal {P}$ of size $n$ containing the origin. Assume that the weight of a Voronoi tile $ C_v$ is given by $ F(C_v)$, where $F$ is a nonnegative functional on Voronoi tiles. In this paper we investigate for some functionals $F$, mainly when $ F(C_v)$ is a polynomial function of the number of faces of $ C_v$, the tail behavior of the maximal weight among polyominoes in $ \Pi_n$: $ F_n = F_n(\mathcal {N}) := \max_{\mathcal {P} \in \Pi_n} \sum_{v \in \mathcal {P}} F(C_v)$. Next we apply our results to study self-avoiding paths, first-passage percolation models and the stabbing number on the dual graph, named the Delaunay triangulation. As the main application we show that first passage percolation has at most linear variance.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "connective constant; Delaunay graph; First passage percolation; greedy animal; Random Voronoi tiling; random walk", } @Article{Procaccia:2012:NSM, author = "Eviatar Procaccia and Ron Rosenthal", title = "The need for speed: maximizing the speed of random walk in fixed environments", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "13:1--13:19", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1800", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1800", abstract = "We study nearest neighbor random walks in fixed environments of $ \mathbb {Z} $ composed of two point types \colon $ (\frac {1}{2}, \frac {1}{2}) $ and$ (p, 1 - p) $ for $ p > \frac {1}{2} $. We show that for every environment with density of $p$ drifts bounded by $ \lambda $ we have $ \limsup_{n \rightarrow \infty } \frac {X_n}{n} \leq (2 p - 1) \lambda $, where $ X_n$ is a random walk in the environment. In addition up to some integer effect the environment which gives the greatest speed is given by equally spaced drifts.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Environment; Random walk; Speed", } @Article{Brightwell:2012:VHD, author = "Graham Brightwell and Malwina Luczak", title = "Vertices of high degree in the preferential attachment tree", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "14:1--14:43", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1803", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1803", abstract = "We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to its degree. We investigate the number $ D_t(\ell) $ of vertices of each degree $ \ell $ at each time $t$, focussing particularly on the case where $ \ell $ is a growing function of $t$. We show that $ D_t(\ell)$ is concentrated around its mean, which is approximately $ 4 t / \ell^3$, for all $ \ell \leq (t / \log t)^{-1 / 3}$; this is best possible up to a logarithmic factor.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "concentration of measure; martingales; preferential attachment; random graphs; web graphs", } @Article{Faggionato:2012:SAN, author = "Alessandra Faggionato", title = "Spectral analysis of {$1$D} nearest-neighbor random walks and applications to subdiffusive trap and barrier models", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "15:1--15:36", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1831", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1831", abstract = "We consider a sequence $ X^{(n)} $, $ n \geq 1 $, of continuous-time nearest-neighbor random walks on the one dimensional lattice $ \mathbb {Z} $. We reduce the spectral analysis of the Markov generator of $ X^{(n)} $ with Dirichlet conditions outside $ (0, n) $ to the analogous problem for a suitable generalized second order differential operator $ - D_{m_n} D_x $, with Dirichlet conditions outside a given interval. If the measures $ d m_n $ weakly converge to some measure $ d m_\infty $, we prove a limit theorem for the eigenvalues and eigenfunctions of $ - D_{m_n}D_x $ to the corresponding spectral quantities of $ - D_{m_\infty } D_x $. As second result, we prove the Dirichlet--Neumann bracketing for the operators $ - D_m D_x $ and, as a consequence, we establish lower and upper bounds for the asymptotic annealed eigenvalue counting functions in the case that $m$ is a self-similar stochastic process. Finally, we apply the above results to investigate the spectral structure of some classes of subdiffusive random trap and barrier models coming from one-dimensional physics.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dirichlet--Neumann bracketing; generalized differential operator; random barrier model; random trap model; random walk; self--similarity; Sturm--Liouville theory", } @Article{Dedecker:2012:RCS, author = "J{\'e}r{\^o}me Dedecker and Paul Doukhan and Florence Merlev{\`e}de", title = "Rates of convergence in the strong invariance principle under projective criteria", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "16:1--16:31", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1849", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1849", abstract = "We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples. We present some applications to a reversible Markov chain, to symmetric random walks on the circle, and to functions of dependent sequences.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "almost sure invariance principle; Markov chains; strong approximations; weak dependence", } @Article{Ruschendorf:2012:OSC, author = "Ludger R{\"u}schendorf and Tomonari Sei", title = "On optimal stationary couplings between stationary processes", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "17:1--17:20", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1797", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1797", abstract = "By a classical result of Gray, Neuhoff and Shields (1975) the rhobar-distance between stationary processes is identified with an optimal stationary coupling problem of the corresponding stationary measures on the infinite product spaces. This is a modification of the optimal coupling problem from Monge--Kantorovich theory. In this paper we derive some general classes of examples of optimal stationary couplings which allow to calculate the rhobar distance in these cases in explicit form. We also extend the rhobar-distance to random fields and to general nonmetric distance functions and give a construction method for optimal stationary cbar-couplings. Our assumptions need in this case a geometric positive curvature condition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$\bar\varrho$-distance; Monge--Kantorovich theory; Optimal stationary couplings; stationary processes", } @Article{Shiraishi:2012:TSR, author = "Daisuke Shiraishi", title = "Two-sided random walks conditioned to have no intersections", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "18:1--18:24", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1742", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1742", abstract = "Let $ S^1, S^2 $ be independent simple random walks in $ \mathbb {Z}^d $ ($ d = 2, 3$) started at the origin. We construct two-sided random walk paths conditioned that $ S^1 [0, \infty) \cap S^2 [1, \infty) = \emptyset $ by showing the existence of the following limit:\par \begin{equation*}\par \lim _{n \rightarrow \infty } P ( \cdot | S^{1}[0, \tau ^{1} ( n) ] \cap S^{2}[1, \tau ^{2}(n) ] = \emptyset ), \par \end{equation*}\par where $ \tau^i(n) = \inf \{ k \ge 0 \colon |S^i (k) | \ge n \} $. Moreover, we give upper bounds of the rate of the convergence. These are discrete analogues of results for Brownian motion obtained by Lawler.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cut points; Invariant measure; Random walks", } @Article{Etore:2012:ETI, author = "Pierre {\'E}tor{\'e} and Miguel Martinez", title = "On the existence of a time inhomogeneous skew {Brownian} motion and some related laws", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "19:1--19:27", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1858", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1858", abstract = "This article is devoted to the construction of a solution for the ``skew inhomogeneous Brownian motion'' equation, which first appear in a seminal paper by Sophie Weinryb (1983). We investigate some laws related to the constructed process. In particular, using the description of the straddling excursion above a deterministic time, we compute the joint law of the process, its local time and its straddling time.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Local time; Skew Brownian motion; Straddling excursion", } @Article{Ethier:2012:PPR, author = "Stewart Ethier and Jiyeon Lee", title = "{Parrondo}'s paradox via redistribution of wealth", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "20:1--20:21", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1867", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1867", abstract = "In Toral's games, at each turn one member of an ensemble of $ N \ge 2 $ players is selected at random to play. He plays either game $ A' $, which involves transferring one unit of capital to a second randomly chosen player, or game $B$, which is an asymmetric game of chance whose rules depend on the player's current capital, and which is fair or losing. Game $ A'$ is fair (with respect to the ensemble's total profit), so the \textit{Parrondo effect} is said to be present if the random mixture $ \gamma A' + (1 - \gamma)B$ (i.e., play game $ A'$ with probability $ \gamma $ and play game $B$ otherwise) is winning. Toral demonstrated the Parrondo effect for $ \gamma = 1 / 2$ using computer simulation. We prove it, establishing a strong law of large numbers and a central limit theorem for the sequence of profits of the ensemble of players for each $ \gamma \in (0, 1)$. We do the same for the nonrandom pattern of games $ (A')^r B^s$ for all integers $ r, s \ge 1$. An unexpected relationship between the random-mixture case and the nonrandom-pattern case occurs in the limit as $ N \to \infty $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem; fundamental matrix; Markov chain; Parrondo's capital-dependent games; stationary distribution; strong law of large numbers", } @Article{Laurent:2012:LDS, author = "Cl{\'e}ment Laurent", title = "Large deviations for self-intersection local times in subcritical dimensions", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "21:1--21:20", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1874", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1874", abstract = "Let $ (X_t, t \geq 0) $ be a simple symmetric random walk on $ \mathbb {Z}^d $ and for any $ x \in \mathbb {Z}^d $, let $ l_t(x) $ be its local time at site $x$. For any $ p > 1$, we denote by$ I_t = \sum \limits_{x \in \mathbb {Z}^d} l_t(x)^p $ the p-fold self-intersection local times (SILT). Becker and K{\"o}nig recently proved a large deviations principle for $ I_t$ for all $ p > 1$ such that $ p(d - 2 / p) < 2$. We extend these results to a broader scale of deviations and to the whole subcritical domain $ p(d - 2) < d$. Moreover, we unify the proofs of the large deviations principle using a method introduced by Castell for the critical case $ p(d - 2) = d$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "intersection local times; Large deviations; self-intersection", } @Article{Casserini:2012:PPC, author = "Matteo Casserini and Freddy Delbaen", title = "Predictable projections of conformal stochastic integrals: an application to {Hermite} series and to {Widder}'s representation", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "22:1--22:14", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1883", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1883", abstract = "In this article, we study predictable projections of stochastic integrals with respect to the conformal Brownian motion, extending the connection between powers of the conformal Brownian motion and the corresponding Hermite polynomials. As a consequence of this result, we then investigate the relation between analytic functions and $ L^p$-convergent series of Hermite polynomials. Finally, our results are applied to Widder's representation for a class of Brownian martingales, retrieving a characterization for the moments of Widder's measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian martingales; conformal Brownian motion; Hermite polynomials; Predictable projections; stochastic integrals; Widder's representation", } @Article{Nutz:2012:QSA, author = "Marcel Nutz", title = "A quasi-sure approach to the control of non-{Markovian} stochastic differential equations", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "23:1--23:23", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1892", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1892", abstract = "We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This value process is characterized by a second order backward SDE, which can be seen as a non-Markovian analogue of the Hamilton--Jacobi Bellman partial differential equation. Moreover, our value process yields a generalization of the $G$-expectation to the context of SDEs.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$G$-expectation; non-Markovian SDE; random $G$-expectation; risk measure; second order BSDE; Stochastic optimal control; volatility uncertainty", } @Article{Song:2012:URM, author = "Yongsheng Song", title = "Uniqueness of the representation for {$G$}-martingales with finite variation", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "24:1--24:15", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1890", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1890", abstract = "Letting $ \{ \delta_n \} $ be a refining sequence of Rademacher functions on the interval $ [0, T] $, we introduce a functional on processes in the $G$-expectation space by $$ [d(K) = \limsup_n \hat {E}[\int_0^T \delta_n(s)d K_s]. $$ We prove that $ d(K) > 0$ if $ K_t = \int_0^t \eta_s d \langle B \rangle_s$ with nontrivial $ \eta \in M^1_G(0, T)$ and that $ d(K) = 0$ if $ K_t = \int_0^t \eta_s d s$ with $ \eta \in M^1_G(0, T)$. This implies the uniqueness of the representation for $G$-martingales with finite variation, which is the main purpose of this article.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$G$-expectation; $G$-martingale; finite variation; representation theorem; uniqueness", } @Article{DeSantis:2012:FOW, author = "Emilio {De Santis} and Fabio Spizzichino", title = "First occurrence of a word among the elements of a finite dictionary in random sequences of letters", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "25:1--25:9", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1878", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1878", abstract = "In this paper we study a classical model concerning occurrence of words in a random sequence of letters from an alphabet. The problem can be studied as a game among $ (m + 1) $ words: the winning word in this game is the one that occurs first. We prove that the knowledge of the first $m$ words results in an advantage in the construction of the last word, as it has been shown in the literature for the cases $ m = 1$ and $ m = 2$ [CZ1, CZ2]. The last word can in fact be constructed so that its probability of winning is strictly larger than $ 1 / (m + 1)$. For the latter probability we will give an explicit lower bound. Our method is based on rather general probabilistic arguments that allow us to consider an arbitrary cardinality for the alphabet, an arbitrary value for $m$ and different mechanisms generating the random sequence of letters.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Competing words; Ergodic; Renewal Theorem; Sub-words", } @Article{Collet:2012:RDD, author = "Francesca Collet and Paolo {Dai Pra}", title = "The role of disorder in the dynamics of critical fluctuations of mean field models", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "26:1--26:40", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1896", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1896", abstract = "The purpose of this paper is to analyze how disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie--Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result concerns the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Disordered models, Interacting particle systems, Mean field interaction, Perturbation theory", } @Article{Martinez:2012:ODP, author = "Miguel Martinez and Denis Talay", title = "One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "27:1--27:30", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1905", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1905", abstract = "In this paper we consider one-dimensional partial differential equations of parabolic type involving a divergence form operator with a discontinuous coefficient and a compatibility transmission condition. We prove existence and uniqueness result by stochastic methods which also allow us to develop a low complexity Monte Carlo numerical resolution method. We get accurate pointwise estimates for the derivatives of the solution from which we get sharp convergence rate estimates for our stochastic numerical method.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Divergence Form Operators; Euler discretization scheme; Monte Carlo methods; Stochastic Differential Equations", } @Article{Erdos:2012:CWD, author = "L{\'a}szl{\'o} Erd{\H{o}}s and Horng-Tzer Yau", title = "A comment on the {Wigner--Dyson--Mehta} bulk universality conjecture for {Wigner} matrices", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "28:1--28:5", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1779", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1779", abstract = "Recently we proved that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we comment on this result in the context of the universality conjectures of Mehta. We show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our previous work.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Wigner random matrix, Mehta, Universality", } @Article{Cerny:2012:IDI, author = "Ji{\v{r}}{\'\i} {\v{C}}ern{\'y} and Serguei Popov", title = "On the internal distance in the interlacement set", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "29:1--29:25", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1936", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1936", abstract = "We prove a shape theorem for the internal (graph) distance on the interlacement set $ \mathcal {I}^u $ of the random interlacement model on $ \mathbb Z^d $, $ d \ge 3 $. We provide large deviation estimates for the internal distance of distant points in this set, and use these estimates to study the internal distance on the range of a simple random walk on a discrete torus.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Capacity; Internal distance; Random interlacement; Shape theorem; Simple random walk", } @Article{Huss:2012:IAM, author = "Wilfried Huss and Ecaterina Sava", title = "Internal aggregation models on comb lattices", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "30:1--30:21", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1940", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1940", abstract = "The two-dimensional comb lattice $ \mathcal {C}_2 $ is a natural spanning tree of the Euclidean lattice $ \mathbb {Z}^2 $. We study three related cluster growth models on $ \mathcal {C}_2 $: internal diffusion limited aggregation (IDLA), in which random walkers move on the vertices of $ \mathcal {C}_2 $ until reaching an unoccupied site where they stop; rotor-router aggregation in which particles perform deterministic walks, and stop when reaching a site previously unoccupied; and the divisible sandpile model where at each vertex there is a pile of sand, for which, at each step, the mass exceeding $1$ is distributed equally among the neighbours. We describe the shape of the divisible sandpile cluster on $ \mathcal {C}_2$, which is then used to give inner bounds for IDLA and rotor-router aggregation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "asymptotic shape; comb lattice; divisible sandpile; growth model; internal diffusion limited aggregation; random walk; rotor-router aggregation; rotor-router walk", } @Article{Cuthbertson:2012:FPC, author = "Charles Cuthbertson and Alison Etheridge and Feng Yu", title = "Fixation probability for competing selective sweeps", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "31:1--31:36", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1954", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1954", abstract = "We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus. We investigate the probability that both mutations will eventually fix in the population. Previous work has dealt with the case where the second mutation to arise confers a smaller benefit than the first. In that case population size plays almost no r{\^o}le. Here we consider the opposite case and observe that, by contrast, the probability of both mutations fixing can be heavily dependent on population size. Indeed the key parameter is $ r N $, the product of the population size and the recombination rate between the two selected loci. If $ r N $ is small, the probability that both mutations fix can be reduced through interference to almost zero while for large $ r N $ the mutations barely influence one another. The main rigorous result is a method for calculating the fixation probability of a double mutant in the large population limit.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "double mutant; fixation probability; selective sweep", } @Article{Chen:2012:GHK, author = "Zhen-Qing Chen and Panki Kim and Renming Song", title = "Global heat kernel estimates for {$ \Delta + \Delta^{\alpha / 2} $} in half-space-like domains", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "32:1--32:32", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1751", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1751", abstract = "Suppose that $ d \ge 1 $ and $ \alpha \in (0, 2) $. In this paper, we establish by using probabilistic methods sharp two-sided pointwise estimates for the Dirichlet heat kernels of $ \{ \Delta + a^\alpha \Delta^{\alpha / 2}; \ a \in (0, 1] \} $ on half-space-like $ C^{1, 1} $ domains for all time $ t > 0 $. The large time estimates for half-space-like domains are very different from those for bounded domains. Our estimates are uniform in $ a \in (0, 1] $ in the sense that the constants in the estimates are independent of $ a \in (0, 1] $. Thus they yield the Dirichlet heat kernel estimates for Brownian motion in half-space-like domains by taking $ a \to 0 $. Integrating the heat kernel estimates with respect to the time variable $t$, we obtain uniform sharp two-sided estimates for the Green functions of $ \{ \Delta + a^\alpha \Delta^{\alpha / 2}; \ a \in (0, 1] \} $ in half-space-like $ C^{1, 1}$ domains in $ R^d$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "symmetric $\alpha$-stable process, heat kernel, transition density, Green function, exit time, L{\'e}vy system, harmonic function, fractional Laplacian, Laplacian, Brownian motion", } @Article{Huber:2012:SRI, author = "Mark Huber and Jenny Law", title = "Simulation reduction of the {Ising} model to general matchings", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "33:1--33:15", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1998", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1998", abstract = "A distribution is tractable if it is possible to approximately sample from the distribution in polynomial time. Here the ferromagnetic Ising model with unidrectional magnetic field is shown to be reducible to a standard distribution on matchings that is tractable. This provides an alternate method to the original Jerrum and Sinclair approach to show that the Ising distribution itself is tractable. Previous reductions of the Ising model to perfect matchings on different graphs exist, but these older distributions are not tractable. Also, the older reductions did not consider an external magnetic field, while the new reduction explictly includes such a field. The new reduction also helps to explain why the idea of canonical paths is so useful in approximately sampling from both problems. In addition, the reduction allows any algorithm for matchings to immediately be applied to the Ising model. For instance, this immediately yields a fully polynomial time approximation scheme for the Ising model on a bounded degree graph with magnetization bounded away from 0, merely by invoking an existing algorithm for matchings.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "canonical paths; fpras; Monte Carlo; simulation reduction", } @Article{Ortmann:2012:LDN, author = "Janosch Ortmann", title = "Large deviations for non-crossing partitions", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "34:1--34:25", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2007", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2007", abstract = "We prove a large deviations principle for the empirical law of the block sizes of a uniformly distributed non-crossing partition. Using well-known bijections we relate this to other combinatorial objects, including Dyck paths, permutations and parking functions. As an application we obtain a variational formula for the maximum of the support of a compactly supported probability measure in terms of its free cumulants, provided these are all non negative. This is useful in free probability theory, where sometimes the R-transform is known but cannot be inverted explicitly to yield the density.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "free probability; Large deviations; non-crossing partitions", } @Article{Pinelis:2012:AGB, author = "Iosif Pinelis", title = "An asymptotically {Gaussian} bound on the {Rademacher} tails", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "35:1--35:22", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2026", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2026", abstract = "An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal distribution, thus affirming a longstanding conjecture by Efron. Applications to sums of general centered uniformly bounded independent random variables and to the Student test are presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Esscher--Cram{\'e}r tilt transform; generalized moments; large deviations; probability inequalities; Rade\-macher random variables; self-normalized sums; Student's test; sums of independent random variables; Tchebycheff--Markov systems", } @Article{Bass:2012:ULP, author = "Richard Bass and Edwin Perkins", title = "On uniqueness in law for parabolic {SPDEs} and infinite-dimensional {SDEs}", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "36:1--36:54", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2049", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2049", abstract = "We give a sufficient conditions for uniqueness in law for the stochastic partial differential equation $$ \frac {\partial u}{\partial t}(x, t) = \frac 12 \frac {\partial^2 u}{\partial x^2}(x, t) + A(u(\cdot, t)) \dot W_{x, t}, $$ where $A$ is an operator mapping $ C[0, 1]$ into itself and $ \dot W$ is a space-time white noise. The approach is to first prove uniquenessfor the martingale problem for the operator\par $$ \mathcal {L} f(x) = \sum_{i, j = 1}^\infty a_{ij}(x) \frac {\partial^2 f}{\partial x^2}(x) - \sum_{i = 1}^\infty \lambda_i x_i \frac {\partial f}{\partial x_i}(x), $$ where $ \lambda_i = c i^2$ and the $ a_{ij}$ is a positive definite bounded operator in Toeplitz form.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Jaffard's theorem; perturbation; stochastic differential equ ations; stochastic partial differential equations; uniqueness", } @Article{Mimica:2012:HIS, author = "Ante Mimica and Panki Kim", title = "{Harnack} inequalities for subordinate {Brownian} motions", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "37:1--37:23", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1930", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1930", abstract = "In this paper, we consider subordinate Brownian motion $X$ in $ \mathbb {R}^d$, $ d \ge 1$, where the Laplace exponent $ \phi $ of the corresponding subordinator satisfies some mild conditions. The scale invariant Harnack inequality is proved for $X$. We first give new forms of asymptotical properties of the L{\'e}vy and potential density of the subordinator near zero. Using these results we find asymptotics of the L{\'e}vy density and potential density of $X$ near the origin, which is essential to our approach. The examples which are covered by our results include geometric stable processes and relativistic geometric stable processes, i.e., the cases when the subordinator has the Laplace exponent\par $$ \phi (\lambda) = \log (1 + \lambda^{\alpha / 2}) \ (0 < \alpha \leq 2) $$ and\par $$ \phi (\lambda) = \log (1 + (\lambda + m^{\alpha / 2})^{2 / \alpha } - m) \ (0 < \alpha < 2, \, m > 0) \, . $$", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "geometric stable process, Green function, Harnack inequality, Poisson kernel, harmonic function, potential, subordinator, subordinate Brownian motion", } @Article{Patie:2012:EFE, author = "Pierre Patie and Mladen Savov", title = "Extended factorizations of exponential functionals of {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "38:1--38:22", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2057", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2057", abstract = "Pardo, Patie, and Savov derived, under mild conditions, a Wiener--Hopf type factorization for the exponential functional of proper L{\'e}vy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed L{\'e}vy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable L{\'e}vy processes. Thus, for example, we show that for any stable process with $ \rho \in (0, \frac {1}{\alpha } - 1] $, where $ \rho \in [0, 1] $ is the positivity parameter and $ \alpha $ is the stable index, then the first passage time has a bounded and non-increasing density on $ \mathbb {R}_+ $. We also generate many instances of integral or power series representations for the law of the exponential functional of L{\'e}vy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed L{\'e}vy process of Wiener--Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Complete monotonicity; Exponential functional; Infinite divisibility; L{\'e}vy processes; Special functions; Stable L{\'e}vy processes; Wiener--Hopf factorizations", } @Article{Hairer:2012:TSA, author = "Martin Hairer and Marc Ryser and Hendrik Weber", title = "Triviality of the {$2$D} stochastic {Allen--Cahn} equation", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "39:1--39:14", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1731", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1731", abstract = "We consider the stochastic Allen--Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to 0, independently of the initial condition. If the intensity of the noise simultaneously converges to 0 at a sufficiently fast rate, then the solutions converge to those of the deterministic equation. At the critical rate, the limiting solution is still deterministic, but it exhibits an additional damping term.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Allen--Cahn equation; SPDEs; stochastic quantisation; white noise", } @Article{Rozkosz:2012:SRE, author = "Andrzej Rozkosz and Leszek Slominski", title = "Stochastic representation of entropy solutions of semilinear elliptic obstacle problems with measure data", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "40:1--40:27", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2062", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2062", abstract = "We consider semilinear obstacle problem with measure data associated with uniformly elliptic divergence form operator. We prove existence and uniqueness of entropy solution of the problem and provide stochastic representation of the solution in terms of some generalized reflected backward stochastic differential equations with random terminal time.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "backward stochastic differential equation; entropy solution; measure data; semilinear elliptic obstacle problem", } @Article{Lacoin:2012:EIP, author = "Hubert Lacoin", title = "Existence of an intermediate phase for oriented percolation", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "41:1--41:17", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1761", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1761", abstract = "We consider the following oriented percolation model of $ \mathbb {N} \times \mathbb {Z}^d $: we equip $ \mathbb {N} \times \mathbb {Z}^d $ with the edge set $ \{ [(n, x), (n + 1, y)] | n \in \mathbb {N}, x, y \in \mathbb {Z}^d \} $, and we say that each edge is open with probability $ p f(y - x) $ where $ f(y - x) $ is a fixed non-negative compactly supported function on $ \mathbb {Z}^d $ with $ \sum_{z \in \mathbb {Z}^d} f(z) = 1 $ and $ p \in [0, \inf f^{-1}] $ is the percolation parameter. Let $ p_c $ denote the percolation threshold ans $ Z_N $ the number of open oriented-paths of length $N$ starting from the origin, and study the growth of $ Z_N$ when percolation occurs. We prove that for if $ d \ge 5$ and the function $f$ is sufficiently spread-out, then there exists a second threshold $ p_c^{(2)} > p_c$ such that $ Z_N / p^N$ decays exponentially fast for $ p \in (p_c, p_c^{(2)})$ and does not so when $ p > p_c^{(2)}$. The result should extend to the nearest neighbor-model for high-dimension, and for the spread-out model when $ d = 3, 4$. It is known that this phenomenon does not occur in dimension 1 and 2.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Directed Polymers; Percolation: Growth model; Phase transition; Random media", } @Article{Samorodnitsky:2012:DSL, author = "Gennady Samorodnitsky and Yi Shen", title = "Distribution of the supremum location of stationary processes", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "42:1--42:17", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2069", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2069", abstract = "The location of the unique supremum of a stationary process on an interval does not need to be uniformly distributed over that interval. We describe all possible distributions of the supremum location for a broad class of such stationary processes. We show that, in the strongly mixing case, this distribution does tend to the uniform in a certain sense as the length of the interval increases to infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bounded variation; global supremum location; stationary process; strong mixing", } @Article{Fill:2012:NBC, author = "James Fill and Svante Janson", title = "The number of bit comparisons used by {Quicksort}: an average-case analysis", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "43:1--43:22", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1812", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1812", abstract = "The analyses of many algorithms and data structures (such as digital search trees) for searching and sorting are based on the representation of the keys involved as bit strings and so count the number of bit comparisons. On the other hand, the standard analyses of many other algorithms (such as Quicksort) are performed in terms of the number of key comparisons. We introduce the prospect of a fair comparison between algorithms of the two types by providing an average-case analysis of the number of bit comparisons required by Quicksort. Counting bit comparisons rather than key comparisons introduces an extra logarithmic factor to the asymptotic average total. We also provide a new algorithm, ``BitsQuick'', that reduces this factor to constant order by eliminating needless bit comparisons.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "average-case analysis of algorithms; Poissonization; Quicksort", } @Article{Ferrari:2012:NCB, author = "Patrik Ferrari and B{\'a}lint Vet{\H{o}}", title = "Non-colliding {Brownian} bridges and the asymmetric tacnode process", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "44:1--44:17", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1811", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1811", abstract = "We consider non-colliding Brownian bridges starting from two points and returning to the same position. These positions are chosen such that, in the limit of large number of bridges, the two families of bridges just touch each other forming a tacnode. We obtain the limiting process at the tacnode, the ``asymmetric tacnode process''. It is a determinantal point process with correlation kernel given by two parameters: (1) the curvature's ratio $ \lambda > 0 $ of the limit shapes of the two families of bridges, (2) a parameter $ \sigma $ controlling the interaction on the fluctuation scale. This generalizes the result for the symmetric tacnode process ($ \lambda = 1 $ case).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "determinantal processes; limit processes; Non-colliding walks; tacnode; universality", } @Article{Ding:2012:CTL, author = "Jian Ding", title = "On cover times for {$2$D} lattices", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "45:1--45:18", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2089", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2089", abstract = "We study the cover time $ \tau_{\mathrm {cov}} $ by (continuous-time) random walk on the {$2$D} box of side length $n$ with wired boundary or on the {$2$D} torus, and show that in both cases with probability approaching $1$ as $n$ increases, $ \sqrt {\tau_{\mathrm {cov}}} = \sqrt {2n^2 [\sqrt {2 / \pi } \log n + O(\log \log n)]}$. This improves a result of Dembo, Peres, Rosen, and Zeitouni (2004) and makes progress towards a conjecture of Bramson and Zeitouni (2009).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cover times; Gaussian free fields; random walks", } @Article{Kevei:2012:ADR, author = "Peter Kevei and David Mason", title = "The asymptotic distribution of randomly weighted sums and self-normalized sums", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "46:1--46:21", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2092", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2092", abstract = "We consider the self-normalized sums $ T_n = \sum_{i = 1}^n X_i Y_i / \sum_{i = 1}^n Y_i $, where $ \{ Y_i \colon i \geq 1 \} $ are non-negative i.i.d. random variables, and $ \{ X_i \colon i \geq 1 \} $ are i.i.d. random variables, independent of $ \{ Y_i \colon i \geq 1 \} $. The main result of the paper is that each subsequential limit law of $ T_n $ is continuous for any non-degenerate $ X_1 $ with finite expectation, if and only if $ Y_1 $ is in the centered Feller class.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Feller class; Self-normalized sums; stable distributions", } @Article{Meleard:2012:NHS, author = "Sylvie M{\'e}l{\'e}ard and Viet Chi Tran", title = "Nonlinear historical superprocess approximations for population models with past dependence", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "47:1--47:32", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2093", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2093", abstract = "We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend on the trait of the ancestors and on its past and allows interactions between individuals through their lineages. We define an interacting historical particle process describing the genealogies of the living individuals; it takes values in the space of point measures on an infinite dimensional c{\`a}dl{\`a}g path space. This individual-based process can be approximated by a nonlinear historical superprocess, under the assumptions of large populations, small individuals and allometric demographies. Because of the interactions, the branching property fails and we use martingale problems and fine couplings between our population and independent branching particles. Our convergence theorem is illustrated by two examples of current interest in biology. The first one relates the biodiversity history of a population and its phylogeny, while the second treats a spatial model where individuals compete through their past trajectories.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Evolution models; Genealogical interacting particle system; Limit theorem; Nonlinear historical superprocess", } @Article{Peterson:2012:LDS, author = "Jonathon Peterson", title = "Large deviations and slowdown asymptotics for one-dimensional excited random walks", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "48:1--48:24", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1726", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1726", abstract = "We study the large deviations of excited random walks on $ \mathbb {Z} $. We prove a large deviation principle for both the hitting times and the position of the random walk and give a qualitative description of the respective rate functions. When the excited random walk is transient with positive speed $ v_0 $, then the large deviation rate function for the position of the excited random walk is zero on the interval $ [0, v_0] $ and so probabilities such as $ P(X_n < n v) $ for $ v \in (0, v_0) $ decay subexponentially. We show that rate of decay for such slowdown probabilities is polynomial of the order $ n^{1 - \delta / 2} $, where $ \delta > 2 $ is the expected total drift per site of the cookie environment.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "excited random walk; large deviations", } @Article{Gozlan:2012:TEI, author = "Nathael Gozlan", title = "Transport-Entropy inequalities on the line", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "49:1--49:18", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1864", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1864", abstract = "We give a necessary and sucient condition for transport entropy inequalities in dimension one. As an application, we construct a new example of a probability distribution verifying Talagrand's {\bf T}2 inequality and not the logarithmic Sobolev inequality.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Optimal transport; Poincar{\'e} inequality; Transport-entropy inequalities", } @Article{Kleptsyn:2012:ESA, author = "Victor Kleptsyn and Aline Kurtzmann", title = "Ergodicity of self-attracting motion", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "50:1--50:37", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2121", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2121", abstract = "We study the asymptotic behaviour of a class of self-attracting motions on $ \mathbb {R}^d $. We prove the decrease of the free energy related to the system and mix it together with stochastic approximation methods. We finally obtain the (limit-quotient) ergodicity of the self-attracting diffusion with a speed of convergence.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "dynamical system; free energy; self-attracting diffusion", } @Article{Baudoin:2012:TES, author = "Fabrice Baudoin and Xuejing Zhang", title = "{Taylor} expansion for the solution of a stochastic differential equation driven by fractional {Brownian} motions", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "51:1--51:21", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2136", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2136", abstract = "We study the Taylor expansion for the solution of a differential equation driven by a multi-dimensional H{\"o}lder path with exponent $ H > 1 / 2 $. We derive a convergence criterion that enables us to write the solution as an infinite sum of iterated integrals on a non empty interval. We apply our deterministic results to stochastic differential equations driven by fractional Brownian motions with Hurst parameter $ H > 1 / 2 $. We also study the convergence in L2 of the stochastic Taylor expansion by using L2 estimates of iterated integrals and Borel--Cantelli type arguments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Taylor expansion, fractional Brownian motion", } @Article{Hairer:2012:SPM, author = "Martin Hairer and David Kelly", title = "Stochastic {PDEs} with multiscale structure", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "52:1--52:38", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1807", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1807", abstract = "We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise. We show that in some cases, in particular when the forcing is given by space time white noise, it may happen that the homogenised SPDE is not what one would expect from existing results for PDEs with more regular forcing terms.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Nguyen:2012:LSV, author = "Hoi Nguyen", title = "On the least singular value of random symmetric matrices", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "53:1--53:19", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2165", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2165", abstract = "Let $ F_n $ be an $n$ by $n$ symmetric matrix whose entries are bounded by $ n^{\gamma }$ for some $ \gamma > 0$. Consider a randomly perturbed matrix $ M_n = F_n + X_n$, where $ X_n$ is a {\it random symmetric matrix} whose upper diagonal entries $ x_{ij}, 1 \leq i \leq j, $ are iid copies of a random variable $ \xi $. Under a very general assumption on $ \xi $, we show that for any $ B > 0$ there exists $ A > 0$ such that $ \mathbb {P}(\sigma_n(M_n) \leq n^{-A}) \le n^{-B}$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random symmetric matrices, least singular values", } @Article{Faller:2012:ASB, author = "Andreas Faller and Ludger R{\"u}schendorf", title = "Approximative solutions of best choice problems", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "54:1--54:22", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2172", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2172", abstract = "We consider the full information best choice problem from a sequence $ X_1, \dots, X_n $ of independent random variables. Under the basic assumption of convergence of the corresponding imbedded point processes in the plane to a Poisson process we establish that the optimal choice problem can be approximated by the optimal choice problem in the limiting Poisson process. This allows to derive approximations to the optimal choice probability and also to determine approximatively optimal stopping times. An extension of this result to the best $m$-choice problem is also given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "best choice problem; optimal stopping; Poisson process", } @Article{Riedler:2012:LTI, author = "Martin Riedler and Mich{\`e}le Thieullen and Gilles Wainrib", title = "Limit theorems for infinite-dimensional piecewise deterministic {Markov} processes. {Applications} to stochastic excitable membrane models", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "55:1--55:48", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1946", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1946", abstract = "We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete random events are globally coupled with continuous space dependent variables solving partial differential equations, e.g., stochastic hybrid models of excitable membranes. We derive a law of large numbers which establishes a connection to deterministic macroscopic models and a martingale central limit theorem which connects the stochastic fluctuations to diffusion processes. As a prerequisite we carry out a thorough discussion of Hilbert space valued martingales associated to the PDMPs. Furthermore, these limit theorems provide the basis for a general Langevin approximation to PDMPs, i.e., stochastic partial differential equations that are expected to be similar in their dynamics to PDMPs. We apply these results to compartmental-type models of spatially extended excitable membranes. Ultimately this yields a system of stochastic partial differential equations which models the internal noise of a biological excitable membrane based on a theoretical derivation from exact stochastic hybrid models.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem; excitable membrane models; infinite-dimensional stochastic processes; law of large numbers; Piecewise Deterministic Markov Processes; random excitable media", } @Article{Brzezniak:2012:SPC, author = "Zdzislaw Brzezniak and Mark Veraar", title = "Is the stochastic parabolicity condition dependent on $p$ and $q$ ?", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "56:1--56:24", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2186", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2186", abstract = "In this paper we study well-posedness of a second order SPDE with multiplicative noise on the torus $ \mathbb {T} = [0, 2 \pi] $. The equation is considered in $ L^p((0, T) \times \Omega; L^q(\mathbb {T})) $ for $ p, q \in (1, \infty) $. It is well-known that if the noise is of gradient type, one needs a stochastic parabolicity condition on the coefficients for well-posedness with $ p = q = 2 $. In this paper we investigate whether the well-posedness depends on $p$ and $q$. It turns out that this condition does depend on $p$, but not on $q$. Moreover, we show that if $ 1 < p < 2$ the classical stochastic parabolicity condition can be weakened.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "blow-up; gradient noise; maximal regularity; mild solution; multiplicative noise; parabolic stochastic evolution; stochastic parabolicity condition; stochastic partial differential equation; strong solution", } @Article{Koval:2012:LRP, author = "Vyacheslav Koval and Ronald Meester and Pieter Trapman", title = "Long-range percolation on the hierarchical lattice", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "57:1--57:21", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1977", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1977", abstract = "We study long-range percolation on the hierarchical lattice of order $N$, where any edge of length $k$ is present with probability $ p_k = 1 - \exp ( - \beta^{-k} \alpha)$, independently of all other edges. For fixed $ \beta $, we show that $ \alpha_c(\beta)$ (the infimum of those $ \alpha $ for which an infinite cluster exists a.s.) is non-trivial if and only if $ N < \beta < N^2$. Furthermore, we show uniqueness of the infinite component and continuity of the percolation probability and of $ \alpha_c(\beta)$ as a function of $ \beta $. This means that the phase diagram of this model is well understood.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "ergodicity; long-range percolation; renormalisation", } @Article{Gayrard:2012:CCP, author = "V{\'e}ronique Gayrard", title = "Convergence of clock process in random environments and aging in {Bouchaud}'s asymmetric trap model on the complete graph", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "58:1--58:33", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2211", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2211", abstract = "In this paper the celebrated arcsine aging scheme of Ben Arous and {\v{C}}ern{\'y} is taken up. Using a brand new approach based on point processes and weak convergence techniques, this scheme is implemented in a broad class of Markov jump processes in random environments that includes Glauber dynamics of discrete disordered systems. More specifically, conditions are given for the underlying clock process (a partial sum process that measures the total time elapsed along paths of a given length) to converge to a subordinator, and consequences for certain time correlation functions are drawn. This approach is applied to Bouchaud's asymmetric trap model on the complete graph for which aging is for the first time proved, and the full, optimal picture, obtained. Application to spin glasses are carried out in follow up papers.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Aging; clock processes; random dynamics; random environments; subordinators; trap models", } @Article{Hryniv:2012:NHR, author = "Ostap Hryniv and Iain MacPhee and Mikhail Menshikov and Andrew Wade", title = "Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "59:1--59:28", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2216", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2216", abstract = "We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non existence of moments for first-passage and last-exit times. In our proofs we also make use of estimates for hitting probabilities and large deviations bounds. Our results are more general than existing results in the literature, which consider only the case of sums of independent (typically, identically distributed) random variables. We do not assume the Markov property. Existing results that we generalize include a circle of ideas related to the Marcinkiewicz--Zygmund strong law of large numbers, as well as more recent work of Kesten and Maller. Our proofs are robust and use martingale methods. We demonstrate the benefit of the generality of our results by applications to some non-classical models, including random walks with heavy-tailed increments on two-dimensional strips, which include, for instance, certain generalized risk processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Heavy-tailed random walks; last exit times; non-homogeneous random walks; passage times; random walks on strips; random walks with internal degrees of freedom; rate of escape; risk process; semimartingales; transience", } @Article{Breuer:2012:NPS, author = "Jonathan Breuer and Maurice Duits", title = "Nonintersecting paths with a staircase initial condition", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "60:1--60:24", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1902", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1902", abstract = "We consider an ensemble of $N$ discrete nonintersecting paths starting from equidistant points and ending at consecutive integers. Our first result is an explicit formula for the correlation kernel that allows us to analyze the process as $ N \to \infty $. In that limit we obtain a new general class of kernels describing the local correlations close to the equidistant starting points. As the distance between the starting points goes to infinity, the correlation kernel converges to that of a single random walker. As the distance to the starting line increases, however, the local correlations converge to the sine kernel. Thus, this class interpolates between the sine kernel and an ensemble of independent particles. We also compute the scaled simultaneous limit, with both the distance between particles and the distance to the starting line going to infinity, and obtain a process with number variance saturation, previously studied by Johansson.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random non-intersecting paths, Determinantal point processes, random tilings", } @Article{Dumaz:2012:CSR, author = "Laure Dumaz", title = "A clever (self-repelling) burglar", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "61:1--61:17", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1758", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1758", abstract = "We derive the following property of the ``true self-repelling motion'', a continuous real-valued self-interacting process $ (X_t, t \ge 0) $ introduced by Balint Toth and Wendelin Werner. Conditionally on its occupation time measure at time one (which is the information about how much time it has spent where before time one), the law of $ X_1 $ is uniform in a certain admissible interval. This contrasts with the corresponding conditional distribution for Brownian motion that had been studied by Warren and Yor.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "local time; self-interacting processes", } @Article{Cohen:2012:QSA, author = "Samuel Cohen", title = "Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "62:1--62:15", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2224", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2224", abstract = "We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our sublinear expectation, we give a simple construction, in a quasi-sure sense, of the (linear) conditional expectations, and hence give a representation for the conditional sublinear expectation. We also show an aggregation property holds, and give an equivalence between consistency and a pasting property of measures.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "aggregation; capacity; dual representation; sublinear expectation", } @Article{Champagnat:2012:DEN, author = "Nicolas Champagnat and Persi Diaconis and Laurent Miclo", title = "On {Dirichlet} eigenvectors for neutral two-dimensional {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "63:1--63:41", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1830", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1830", abstract = "We consider a general class of discrete, two-dimensional Markov chains modeling the dynamics of a population with two types, without mutation or immigration, and neutral in the sense that type has no influence on each individual's birth or death parameters. We prove that all the eigenvectors of the corresponding transition matrix or infinitesimal generator $ \Pi $ can be expressed as the product of ``universal'' polynomials of two variables, depending on each type's size but not on the specific transitions of the dynamics, and functions depending only on the total population size. These eigenvectors appear to be Dirichlet eigenvectors for $ \Pi $ on the complement of triangular subdomains, and as a consequence the corresponding eigenvalues are ordered in a specific way. As an application, we study the quasistationary behavior of finite, nearly neutral, two-dimensional Markov chains, absorbed in the sense that $0$ is an absorbing state for each component of the process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coexistence; Dirichlet eigenvalue; Dirichlet eigenvector; Hahn polynomials; multitype population dynamics; neutral Markov chain; quasi-stationary distribution; two-dimensional difference equation; Yaglom limit", } @Article{Yang:2012:CED, author = "Yanrong Yang and Guangming Pan", title = "The convergence of the empirical distribution of canonical correlation coefficients", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "64:1--64:13", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2239", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2239", abstract = "Suppose that $ \{ X_{jk}, j = 1, \cdots, p_1; k = 1, \cdots, n \} $ are independent and identically distributed (i.i.d) real random variables with $ E X_{11} = 0 $ and $ E X_{11}^2 = 1 $, and that $ \{ Y_{jk}, j = 1, \cdots, p_2; k = 1, \cdots, n \} $ are i.i.d real random variables with $ E Y_{11} = 0 $ and $ E Y_{11}^2 = 1 $, and that $ \{ X_{jk}, j = 1, \cdots, p_1; k = 1, \cdots, n \} $ are independent of $ \{ Y_{jk}, j = 1, \cdots, p_2; k = 1, \cdots, n \} $. This paper investigates the canonical correlation coefficients $ r_1 \geq r_2 \geq \cdots \geq r_{p_1} $, whose squares $ \lambda_1 = r_1^2, \lambda_2 = r_2^2, \cdots, \lambda_{p_1} = r_{p_1}^2 $ are the eigenvalues of the matrix\par \begin{equation*} S_{xy} = A_x^{-1} A_{xy} A_y^{-1} A_{xy}^{T}, \end{equation*}\par where\par \begin{equation*} A_x=\frac{1}{n}\sum^{n}_{k=1}x_kx_k^{T},\\ A_y=\frac{1}{n}\sum^{n}_{k=1}y_ky_k^{T},\\ A_{xy}=\frac{1}{n}\sum^{n}_{k=1}x_ky_k^{T}, \end{equation*}\par and\par \begin{equation*} x_k=(X_{1k}, \cdots, X_{p_1k})^{T},\\ y_k=(Y_{1k}, \cdots, Y_{p_2k})^{T}, k=1, \cdots, n. \end{equation*}\par When $ p_1 \rightarrow \infty $, $ p_2 \rightarrow \infty $ and $ n \rightarrow \infty $ with $ \frac {p_1}{n} \rightarrow c_1 $, $ \frac {p_2}{n} \rightarrow c_2 $, $ c_1, c_2 \in (0, 1) $, it is proved that the empirical distribution of $ r_1, r_2, \cdots, r_{p_1} $ converges, with probability one, to a fixed distribution under the finite second moment condition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Canonical correlation coefficients; Empirical spectral distribution; Lindeberg's method.; Random matrix; Stieltjes transform", } @Article{Kruse:2012:ORS, author = "Raphael Kruse and Stig Larsson", title = "Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "65:1--65:19", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2240", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2240", abstract = "This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic parabolic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions and certain linear growth bounds. It is shown that the mild solution has the same optimal regularity properties as the stochastic convolution. The proof is elementary and makes use of existing results on the regularity of the solution, in particular, the H{\"o}lder continuity with a non-optimal exponent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "H{\"o}lder continuity; linear growth bound; Lipschitz nonlinearities; multiplicative noise; SPDE; temporal and spatial regularity", } @Article{Fulman:2012:SMH, author = "Jason Fulman", title = "{Stein}'s method, heat kernel, and traces of powers of elements of compact {Lie} groups", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "66:1--66:16", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2251", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2251", abstract = "Combining Stein's method with heat kernel techniques, we show that the trace of the jth power of an element of U(n, C), USp(n, C), or SO(n, R) has a normal limit with error term C j/n, with C an absolute constant. In contrast to previous works, here j may be growing with n. The technique might prove useful in the study of the value distribution of approximate eigenfunctions of Laplacians.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random matrix, Stein's method, heat kernel", } @Article{Fang:2012:BRW, author = "Ming Fang and Ofer Zeitouni", title = "Branching random walks in time inhomogeneous environments", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "67:1--67:18", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2253", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2253", abstract = "We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change over time macroscopically. We find the asymptotics of the maximum up to an $ O_P(1) $ (stochastically bounded) error, and focus on the following phenomena: the profile of the variance matters, both to the leading (velocity) term and to the logarithmic correction term, and the latter exhibits a phase transition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching random walks; time inhomogeneous environments", } @Article{Hammond:2012:ETT, author = "Alan Hammond and Elchanan Mossel and G{\'a}bor Pete", title = "Exit time tails from pairwise decorrelation in hidden {Markov} chains, with applications to dynamical percolation", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "68:1--68:16", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2229", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2229", abstract = "Consider a Markov process $ \omega_t $ at stationarity and some event $ \mathcal {C} $ (a subset of the state-space of the process). A natural measure of correlations in the process is the pairwise correlation $ \mathbb {P}[\omega_0, \omega_t \in \mathcal {C}] - \mathbb {P}[\omega_0 \in \mathcal {C}]^2 $. A second natural measure is the probability of the continual occurrence event $ \big \{ \omega_s \in \mathcal {C}, \, \forall \, s \in [0, t] \big \} $. We show that for reversible Markov chains, and any event $ \mathcal {C} $, pairwise decorrelation of the event $ \mathcal {C} $ implies a decay of the probability of the continual occurrence event $ \big \{ \omega_s \in \mathcal {C} \, \forall \, s \in [0, t] \big \} $ as $ t \to \infty $. We provide examples showing that our results are often sharp.\par Our main applications are to dynamical critical percolation. Let $ \mathcal {C} $ be the left-right crossing event of a large box, and let us scale time so that the expected number of changes to $ \mathcal {C} $ is order 1 in unit time. We show that the continual connection event has superpolynomial decay. Furthermore, on the infinite lattice without any time scaling, the first exceptional time with an infinite cluster appears with an exponential tail.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "decorrelation, hidden Markov chains, hitting and exit times, spectral gap, dynamical percolation, exceptional times, scaling limits", } @Article{Profeta:2012:PNR, author = "Christophe Profeta", title = "Penalizing null recurrent diffusions", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "69:1--69:23", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2267", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2267", abstract = "We present some limit theorems for the normalized laws (with respect to functionals involving last passage times at a given level $a$ up to time $t$) of a large class of null recurrent diffusions. Our results rely on hypotheses on the L{\'e}vy measure of the diffusion inverse local time at 0. As a special case, we recover some of the penalization results obtained by Najnudel, Roynette and Yor in the (reflected) Brownian setting.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "inverse local time; last passage times; null recurrent diffusions; Penalization", } @Article{Oliveira:2012:MHT, author = "Roberto Oliveira", title = "Mixing and hitting times for finite {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "70:1--70:12", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2274", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2274", abstract = "Let $ 0 < \alpha < 1 / 2 $. We show that the mixing time of a continuous-time Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of the state space with stationary measure $ \geq \alpha $. Suitably modified results hold in discrete time and/or without the reversibility assumption. The key technical tool in the proof is the construction of random set $A$ such that the hitting time of $A$ is a light-tailed stationary time for the chain. We note that essentially the same results were obtained independently by Peres and Sousi.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "hitting times; Markov chains.; Mixing times", } @Article{Hutzenthaler:2012:IDT, author = "Martin Hutzenthaler", title = "Interacting diffusions and trees of excursions: convergence and comparison", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "71:1--71:49", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2278", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2278", abstract = "We consider systems of interacting diffusions with local population regulation representing populations on countably many islands. Our main result shows that the total mass process of such a system is bounded above by the total mass process of a tree of excursions with appropriate drift and diffusion coefficients. As a corollary, this entails a sufficient, explicit condition for extinction of the total mass as time tends to infinity. On the way to our comparison result, we establish that systems of interacting diffusions with uniform migration between finitely many islands converge to a tree of excursions as the number of islands tends to infinity. In the special case of logistic branching, this leads to a duality between a tree of excursions and the solution of a McKean--Vlasov equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "excursion measure; extinction; Island model; many-demes-limit; McKean--Vlasov limit; mean field model; propagation of chaos; virgin island model", } @Article{Kobylanski:2012:OST, author = "Magdalena Kobylanski and Marie-Claire Quenez", title = "Optimal stopping time problem in a general framework", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "72:1--72:28", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2262", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2262", abstract = "We study the optimal stopping time problem $ v(S) = {\rm ess} \sup_{\theta \geq S} E[\phi (\theta)| \mathcal {F}_S] $, for any stopping time $S$, where the reward is given by a family $ (\phi (\theta), \theta \in \mathcal {T}_0)$ \emph{of non negative random variables} indexed by stopping times. We solve the problem under weak assumptions in terms of integrability and regularity of the reward family. More precisely, we only suppose $ v(0) < + \infty $ and $ (\phi (\theta), \theta \in \mathcal {T}_0)$ upper semicontinuous along stopping times in expectation. We show the existence of an optimal stopping time and obtain a characterization of the minimal and the maximal optimal stopping times. We also provide some local properties of the value function family. All the results are written in terms of families of random variables and are proven by only using classical results of the Probability Theory", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "American options; optimal stopping; supermartingale", } @Article{Liu:2012:CSP, author = "Huili Liu and Xiaowen Zhou", title = "The compact support property for the {$ \Lambda $}-{Fleming--Viot} process with underlying {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "73:1--73:20", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1928", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1928", abstract = "Using the lookdown construction of Donnelly and Kurtz we prove that, at any fixed positive time, the $ \Lambda $-Fleming--Viot process with underlying Brownian motion has a compact support provided that the corresponding $ \Lambda $-coalescent comes down from infinity not too slowly. We also find both upper bound and lower bound on the Hausdorff dimension for the support.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$\Lambda$-coalescent; $\Lambda$-Fleming--Viot process; compact support property; lookdown construction", } @Article{Basse-OConnor:2012:MPS, author = "Andreas Basse-O'Connor and Svend-Erik Graversen and Jan Pedersen", title = "Multiparameter processes with stationary increments: Spectral representation and integration", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "74:1--74:21", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2287", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2287", abstract = "In this article, a class of multiparameter processes with wide-sense stationary increments is studied. The content is as follows. (1) The spectral representation is derived; in particular, necessary and sufficient conditions for a measure to be a spectral measure is given. The relations to a commonly used class of processes, studied e.g., by Yaglom, is discussed. (2) Some classes of deterministic integrands, here referred to as predomains, are studied in detail. These predomains consist of functions or, more generally, distributions. Necessary and sufficient conditions for completeness of the predomains are given. (3) In a framework covering the classical Walsh--Dalang theory of a temporal-spatial process which is white in time and colored in space, a class of predictable integrands is considered. Necessary and sufficient conditions for completeness of the class are given, and this property is linked to a certain martingale representation property.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "integration; Multiparameter processes; spectral representation; stationary increments", } @Article{Dembo:2012:CLT, author = "Amir Dembo and Nike Sun", title = "Central limit theorem for biased random walk on multi-type {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "75:1--75:40", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2294", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2294", abstract = "Let $ \mathcal {T} $ be a rooted supercritical multi-type Galton--Watson (MGW) tree with types coming from a finite alphabet, conditioned to non-extinction. The $ \lambda $-biased random walk $ (X_t)_{t \ge 0}$ on $ \mathcal {T}$ is the nearest-neighbor random walk which, when at a vertex $v$ with $ d_v$ offspring, moves closer to the root with probability $ \lambda / (\lambda + d_v)$, and to each of the offspring with probability $ 1 / (\lambda + d_v)$. This walk is recurrent for $ \lambda \ge \rho $ and transient for $ 0 \leq \lambda < \rho $, with $ \rho $ the Perron--Frobenius eigenvalue for the (assumed) irreducible matrix of expected offspring numbers. Subject to finite moments of order $ p > 4$ for the offspring distributions, we prove the following quenched CLT for $ \lambda $-biased random walk at the critical value $ \lambda = \rho $: for almost every $ \mathcal {T}$, the process $ |X_{\lfloor nt \rfloor }| / \sqrt {n}$ converges in law as $ n \to \infty $ to a reflected Brownian motion rescaled by an explicit constant. This result was proved under some stronger assumptions by Peres--Zeitouni (2008) for single-type Galton--Watson trees. Following their approach, our proof is based on a new explicit description of a reversing measure for the walk from the point of view of the particle (generalizing the measure constructed in the single-type setting by Peres--Zeitouni), and the construction of appropriate harmonic coordinates. In carrying out this program we prove moment and conductance estimates for MGW trees, which may be of independent interest. In addition, we extend our construction of the reversing measure to a biased random walk with random environment (RWRE) on MGW trees, again at a critical value of the bias. We compare this result against a transience-recurrence criterion for the RWRE generalizing a result of Faraud (2011) for Galton--Watson trees.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "biased random walk; central limit theorem; Multi-type Galton--Watson tree; random walk with random environment", } @Article{Tugaut:2012:EPM, author = "Julian Tugaut", title = "Exit problem of {McKean--Vlasov} diffusions in convex landscapes", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "76:1--76:26", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1914", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1914", abstract = "The exit time and the exit location of a non-Markovian diffusion is analyzed. More particularly, we focus on the so-called self-stabilizing process. The question has been studied by Herrmann, Imkeller and Peithmann (in 2008) with results similar to those by Freidlin and Wentzell. We aim to provide the same results by a more intuitive approach and without reconstructing the proofs of Freidlin and Wentzell. Our arguments are as follows. In one hand, we establish a strong version of the propagation of chaos which allows to link the exit time of the McKean--Vlasov diffusion and the one of a particle in a mean-field system. In the other hand, we apply the Freidlin--Wentzell theory to the associated mean field system, which is a Markovian diffusion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Exit location; Exit time; Granular media equation; Interacting particle systems; Large deviations; Propagation of chaos; Self-stabilizing diffusion", } @Article{Gnedin:2012:RCC, author = "Alexander Gnedin and Alexander Iksanov", title = "Regenerative compositions in the case of slow variation: A renewal theory approach", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "77:1--77:19", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2002", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2002", abstract = "A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies on the asymptotics of the number of blocks $ K_n $ in the composition of integer $n$, in the case when the L{\'e}vy measure of the subordinator has a property of slow variation at $0$. Using tools from the renewal theory the limit laws for $ K_n$ are obtained in terms of integrals involving the Brownian motion or stable processes. In other words, the limit laws are either normal or other stable distributions, depending on the behavior of the tail of L{\'e}vy measure at $ \infty $. Similar results are also derived for the number of singleton blocks.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "first passage time; number of blocks; regenerative composition; renewal theory; weak convergence", } @Article{Guillotin-Plantard:2012:RTR, author = "Nadine Guillotin-Plantard and Fran{\c{c}}oise P{\`e}ne", title = "Renewal theorems for random walk in random scenery", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "78:1--78:22", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1843", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1843", abstract = "In this work, we establish renewal-type theorems, with precise asymptotics, in the context of random walk in random sceneries.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "local time; Random walk in random scenery; renewal theory; stable distribution", } @Article{Sobieczky:2012:BAR, author = "Florian Sobieczky", title = "Bounds for the annealed return probability on large finite percolation graphs", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "79:1--79:17", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2329", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2329", abstract = "Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation and the associated heavy-tailed cluster size distributions. The upper bound relies on the fact that cartesian products of finite graphs with cycles of a certain minimal size are Hamiltonian. For critical Bernoulli bond percolation on the homogeneous tree this bound is sharp. The asymptotic type of the expected return probability for large times $t$ in this case is of order $ t^{-3 / 4}$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Annealed Return Probability; Anomalous Diffusion; Critical Invariant Percolation; Integrated Density of States; Number of open clusters per vertex; Random walks", } @Article{Athreya:2012:SBA, author = "Siva Athreya and Jan Swart", title = "Systems of branching, annihilating, and coalescing particles", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "80:1--80:32", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2003", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2003", abstract = "This paper studies systems of particles following independent random walks and subject to annihilation, binary branching, coalescence, and deaths. In the case without annihilation, such systems have been studied in our 2005 paper ``Branching-coalescing particle systems''. The case with annihilation is considerably more difficult, mainly as a consequence of the non monotonicity of such systems and a more complicated duality. Nevertheless, we show that adding annihilation does not significantly change the long-time behavior of the process and in fact, systems with annihilation can be obtained by thinning systems without annihilation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Reaction-diffusion process, branching, coalescence, annihilation, thinning, Poissonization", } @Article{Werness:2012:RSL, author = "Brent Werness", title = "Regularity of {Schramm--Loewner} evolutions, annular crossings, and rough path theory", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "81:1--81:21", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2331", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2331", abstract = "When studying stochastic processes, it is often fruitful to understand several different notions of regularity. One such notion is the optimal H{\"o}lder exponent obtainable under reparametrization. In this paper, we show that chordal $ \mathrm {SLE}_\kappa $ in the unit disk for $ \kappa \leq 4 $ can be reparametrized to be H{\"o}lder continuous of any order up to $ 1 / (1 + \kappa / 8) $.\par From this, we obtain that the Young integral is well defined along such $ \mathrm {SLE}_\kappa $ paths with probability one, and hence that $ \mathrm {SLE}_\kappa $ admits a path-wise notion of integration. This allows us to consider the expected signature of $ \mathrm {SLE} $, as defined in rough path theory, and to give a precise formula for its first three gradings.\par The main technical result required is a uniform bound on the probability that an $ \mathrm {SLE}_\kappa $ crosses an annulus $k$-distinct times.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "H{\"o}lder regularity; rough path theory; Schramm--Loewner Evolutions; signature; Young integral", } @Article{Basu:2012:JCS, author = "Riddhipratim Basu and Arup Bose and Shirshendu Ganguly and Rajat Hazra", title = "Joint convergence of several copies of different patterned random matrices", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "82:1--82:33", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1970", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1970", abstract = "We study the joint convergence of independent copies of several patterned matrices in the non-commutative probability setup. In particular, joint convergence holds for the well known Wigner, Toeplitz, Hankel, Reverse Circulant and Symmetric Circulant matrices. We also study some properties of the limits. In particular, we show that copies of Wigner becomes asymptotically free with copies of any of the above other matrices.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random matrices, free probability, joint convergence, patterned matrices, Toeplitz matrix, Hankel matrix, Reverse Circulant matrix, Symmetric Circulant matrix, Wigner matrix", } @Article{Kwasnicki:2012:STS, author = "Mateusz Kwa{\'s}nicki", title = "Spectral theory for symmetric one-dimensional {L{\'e}vy} processes killed upon hitting the origin", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "83:1--83:29", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2013", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2013", abstract = "Spectral theory for transition operators of one-dimensional symmetric L{\'e}vy process killed upon hitting the origin is studied. Under very mild assumptions, an integral-type formula for eigenfunctions is obtained, and eigenfunction expansion of transition operators and the generator is proved. As an application, and the primary motivation, integral fomulae for the transition density and the distribution of the hitting time of the origin are given in terms of the eigenfunctions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "first hitting time; L{\'e}vy process; spectral theory", } @Article{Belaribi:2012:UFP, author = "Nadia Belaribi and Francesco Russo", title = "Uniqueness for {Fokker--Planck} equations with measurable coefficients and applications to the fast diffusion equation", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "84:1--84:28", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2349", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2349", abstract = "The object of this paper is the uniqueness for a $d$-dimensional Fokker--Planck type equation with inhomogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic representation of the so-called Barenblatt's solution of the fast diffusion equation which is the partial differential equation $ \partial_t u = \partial^2_{xx} u^m$ with $ m \in]0, 1 [$. Together with the mentioned Fokker--Planck equation, we make use of small time density estimates uniformly with respect to the initial condition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fast diffusion; Fokker--Planck; non-linear diffusion; probabilistic representation; stochastic particle algorithm", } @Article{Gallesco:2012:RWU, author = "Christophe Gallesco and Serguei Popov", title = "Random walks with unbounded jumps among random conductances {I}: Uniform quenched {CLT}", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "85:1--85:22", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1826", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1826", abstract = "We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched {\em uniform} invariance principle for the random walk. This means that the rescaled trajectory of length $n$ is (in a certain sense) close enough to the Brownian motion, uniformly with respect to the choice of the starting location in an interval of length $ O(\sqrt {n}) $ around the origin.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "ergodic environment; exit distribution; hitting probabilities; unbounded jumps", } @Article{Masse:2012:RNS, author = "Bruno Mass{\'e} and Dominique Schneider", title = "Random number sequences and the first digit phenomenon", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "86:1--86:17", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1900", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1900", abstract = "The sequences of mantissa of positive integers and of prime numbers are known not to be distributed as Benford's law in the sense of the natural density. We show that we can correct this defect by selecting the integers or the primes by means of an adequate random process and we investigate the rate of convergence. Our main tools are uniform bounds for deterministic and random trigonometric polynomials. We then adapt the random process to prove the same result for logarithms and iterated logarithms of integers. Finally we show that, in many cases, the mantissa law of the $n$ th randomly selected term converges weakly to the Benford's law.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Benford's law; density; mantissa; weak convergence", } @Article{Ben-Ari:2012:PEB, author = "Iddo Ben-Ari", title = "Principal eigenvalue for {Brownian} motion on a bounded interval with degenerate instantaneous jumps", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "87:1--87:13", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1791", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1791", abstract = "We consider a model of Brownian motion on a bounded open interval with instantaneous jumps. The jumps occur at a spatially dependent rate given by a positive parameter times a continuous function positive on the interval and vanishing on its boundary. At each jump event the process is redistributed uniformly in the interval. We obtain sharp asymptotic bounds on the principal eigenvalue for the generator of the process as the parameter tends to infinity. Our work answers a question posed by Arcusin and Pinsky.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "brownian motion; principal eigenvalue; random space-dependent jumps", } @Article{Bao:2012:TWL, author = "Zhigang Bao and Guangming Pan and Wang Zhou", title = "{Tracy--Widom} law for the extreme eigenvalues of sample correlation matrices", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "88:1--88:32", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1962", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1962", abstract = "Let the sample correlation matrix be $ W = Y Y^T $ , where $ Y = (y_{ij})_{p, n} $ with $ y_{ij} = x_{ij} / \sqrt {\sum_{j = 1}^nx_{ij}^2} $. We assume $ \{ x_{ij} \colon 1 \leq i \leq p, 1 \leq j \leq n \} $ to be a collection of independent symmetrically distributed random variables with sub-exponential tails. Moreover, for any $i$, we assume $ x_{ij}, 1 \leq j \leq n$ to be identically distributed. We assume $ 0 < p < n$ and $ p / n \rightarrow y$ with some $ y \in (0, 1)$ as $ p, n \rightarrow \infty $. In this paper, we provide the Tracy--Widom law ($ T W_1$) for both the largest and smallest eigenvalues of $W$. If $ x_{ij}$ are i.i.d. standard normal, we can derive the $ T W_1$ for both the largest and smallest eigenvalues of the matrix $ \mathcal {R} = R R^T$, where $ R = (r_{ij})_{p, n}$ with $ r_{ij} = (x_{ij} - \bar x_i) / \sqrt {\sum_{j = 1}^n(x_{ij} - \bar x_i)^2}$, $ \bar x_i = n^{-1} \sum_{j = 1}^n x_{ij}$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "extreme eigenvalues; sample correlation matrices; sample covariance matrices; Stieltjes transform; Tracy--Widom law", } @Article{Leon:2012:ALS, author = "Jorge Leon and David M{\'a}rquez-Carreras and Josep Vives", title = "Anticipating linear stochastic differential equations driven by a {L{\'e}vy} process", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "89:1--89:26", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1910", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1910", abstract = "In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a L{\'e}vy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformation on Wiener space and developed by Buckdahn [7] to the canonical L{\'e}vy space, which is introduced in [25].", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Canonical L{\'e}vy space; Girsanov transformations; L{\'e}vy and Poisson measures; Malliavin calculus; Pathwise integral; Skorohod integral", } @Article{Barbour:2012:CLA, author = "Andrew Barbour and Malwina Luczak", title = "Central limit approximations for {Markov} population processes with countably many types", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "90:1--90:16", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1760", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1760", abstract = "When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $ \ell_1 $ norm.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit approximation; countably many types; Epidemic models; Markov population processes; metapopulation processes", } @Article{Schweinsberg:2012:DEB, author = "Jason Schweinsberg", title = "Dynamics of the evolving {Bolthausen--Sznitman} coalescent", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "91:1--91:50", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2378", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2378", abstract = "Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the population. As time goes forward, the genealogy of the population evolves, leading to what is known as an evolving coalescent. We will study the evolving coalescent for populations whose genealogy can be described by the Bolthausen Sznitman coalescent. We obtain the limiting behavior of the evolution of the time back to the most recent common ancestor and the total length of the branches in the tree. By similar methods, we also obtain a new result concerning the number of blocks in the Bolthausen--Sznitman coalescent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bolthausen--Sznitman coalescent; most recent common ancestor; total branch length", } @Article{Nagahata:2012:LBE, author = "Yukio Nagahata", title = "Lower bound estimate of the spectral gap for simple exclusion process with degenerate rates", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "92:1--92:19", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1916", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1916", abstract = "We consider exclusion process with degenerate rates in a finite torus with size $n$. This model is a simplified model for some peculiar phenomena of the ``glassy'' dynamics. We prove that the spectral gap is bounded below by $ C \rho^4 / n^2$, where $ \rho = k / n$ denotes the density of particle and $C$ does not depend on $n$ nor $ \rho $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "degenerate rate; exclusion process; spectral gap", } @Article{Benjamini:2012:ETS, author = "Itai Benjamini and Nicolas Curien", title = "Ergodic theory on stationary random graphs", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "93:1--93:20", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2401", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2401", abstract = "A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random graphs of subexponential growth are almost surely Liouville, that is, admit no non constant bounded harmonic functions. Applications include the uniform infinite planar quadrangulation and long-range percolation clusters.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Entropy; Ergodic Theory; Liouville Property; Simple random walk; Stationary random graph", } @Article{Doring:2012:JTS, author = "Leif D{\"o}ring and Matyas Barczy", title = "Jump type {SDEs} for self-similar processes", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "94:1--94:39", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2402", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2402", abstract = "We present a new approach to positive self-similar Markov processes (pssMps) by reformulating Lamperti's transformation via jump type SDEs. As applications, we give direct constructions of pssMps (re)started continuously at zero if the Lamperti transformed L{\'e}vy process is spectrally negative. Our paper can be seen as a continuation of similar studies for continuous state branching processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "L{\'e}vy process, self-similar Markov process, Lamperti's transformation, jump type SDEs", } @Article{Liu:2012:FER, author = "Dangzheng Liu and Xin Sun and Zhengdong Wang", title = "Fluctuations of eigenvalues for random {Toeplitz} and related matrices", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "95:1--95:22", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2006", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2006", abstract = "Consider random symmetric Toeplitz matrices $ T_n = (a_{i - j})_{i, j = 1}^n $ with matrix entries $ a_j, j = 0, 1, 2, \cdots, $ being independent real random variables such that\par $$ \mathbb {E}[a_j] = 0, \ \ \mathbb {E} [|a_j|^2] = 1 \ \mathrm {for} \, \ \ j = 0, 1, 2, \cdots, $$ (homogeneity of 4-th moments)\par $$ \kappa = \mathbb {E} [|a_j|^4], $$ and further (uniform boundedness)\par $$ \sup \limits_{j \geq 0} \mathbb {E} [|a_j|^k] = C_k < \infty \ \ \mathrm {for} \ \ \ k \geq 3. $$ Under the assumption of $ a_0 \equiv 0 $, we prove a central limit theorem for linear statistics of eigenvalues for a fixed polynomial with degree at least 2. Without this assumption, the CLT can be easily modified to a possibly non-normal limit law. In a special case where $ a_j $'s are Gaussian, the result has been obtained by Chatterjee for some test functions. Our derivation is based on a simple trace formula for Toeplitz matrices and fine combinatorial analysis. Our method can apply to other related random matrix models, including Hermitian Toeplitz and symmetric Hankel matrices. Since Toeplitz matrices are quite different from Wigner and Wishart matrices, our results enrich this topic.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central limit theorem; Hankel matrix; Linear statistics of eigenvalues; Random matrices; Toeplitz (band) matrix", } @Article{Athreya:2012:PLF, author = "Avanti Athreya and Tiffany Kolba and Jonathan Mattingly", title = "Propagating {Lyapunov} functions to prove noise-induced stabilization", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "96:1--96:38", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2410", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2410", abstract = "We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the addition of additive noise in the vertical direction leads to a unique invariant probability measure to which the system converges at a uniform, exponential rate. These facts are established primarily through the construction of a Lyapunov function which we generate as the solution to a sequence of Poisson equations. Unlike a number of other works, however, our Lyapunov function is constructed in a systematic way, and we present a meta-algorithm we hope will be applicable to other problems. We conclude by proving positivity properties of the transition density by using Malliavin calculus via some unusually explicit calculations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "SDEs, Lyapunov Functions, Invariant Measures, Stochastic Stabilization", } @Article{Mourrat:2012:QCL, author = "Jean-Christophe Mourrat", title = "A quantitative central limit theorem for the random walk among random conductances", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "97:1--97:17", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2414", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2414", abstract = "We consider the random walk among random conductances on $ \mathbb {Z}^d $. We assume that the conductances are independent, identically distributed and uniformly bounded away from $0$ and infinity. We obtain a quantitative version of the central limit theorem for this random walk, which takes the form of a {Berry--Ess{\'e}en} estimate with speed $ t^{-1 / 10}$ for $ d \leq 2$, and speed $ t^{-1 / 5}$ for $ d \ge 3$, up to logarithmic corrections.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem; homogenization; Random walk among random conductances; {Berry--Ess{\'e}en} estimate", } @Article{Dolinsky:2012:NSE, author = "Yan Dolinsky", title = "Numerical schemes for {$G$}-Expectations", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "98:1--98:15", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2284", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2284", abstract = "We consider a discrete time analog of $G$-expectations and we prove that in the case where the time step goes to zero the corresponding values converge to the original $G$-expectation. Furthermore we provide error estimates for the convergence rate. This paper is continuation of Dolinsky, Nutz, and Soner (2012). Our main tool is a strong approximation theorem which we derive for general discrete time martingales.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$G$-expectations, volatility uncertainty, strong approximation theorems", } @Article{Angel:2012:PTR, author = "Omer Angel and Vadim Gorin and Alexander Holroyd", title = "A pattern theorem for random sorting networks", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "99:1--99:16", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2448", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2448", abstract = "A sorting network is a shortest path from $ 12 \cdots n $ to $ n \cdots 21 $ in the Cayley graph of the symmetric group $ S_n $ generated by nearest-neighbor swaps. A pattern is a sequence of swaps that forms an initial segment of some sorting network. We prove that in a uniformly random $n$-element sorting network, any fixed pattern occurs in at least $ c n^2$ disjoint space-time locations, with probability tending to $1$ exponentially fast as $ n \to \infty $. Here $c$ is a positive constant which depends on the choice of pattern. As a consequence, the probability that the uniformly random sorting network is geometrically realizable tends to $0$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "pattern; random sorting; reduced word; Sorting network; Young tableau", } @Article{Shao:2012:HIS, author = "Jinghai Shao and Feng-Yu Wang and Chenggui Yuan", title = "{Harnack} inequalities for stochastic (functional) differential equations with non-{Lipschitzian} coefficients", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "100:1--100:18", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2140", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2140", abstract = "By using coupling arguments, Harnack type inequalities are established for a class of stochastic (functional) differential equations with multiplicative noises and non-Lipschitzian coefficients. To construct the required couplings, two results on existence and uniqueness of solutions on an open domain are presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "existence and uniqueness; Harnack inequality; log-Harnack inequality; stochastic (functional) differential equation", } @Article{Adamczak:2012:MEC, author = "Rados{\l}aw Adamczak and Olivier Gu{\'e}don and Rafa{\l} Lata{\l}a and Alexander Litvak and Krzysztof Oleszkiewicz and Alain Pajor and Nicole Tomczak-Jaegermann", title = "Moment estimates for convex measures", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "101:1--101:19", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2150", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2150", abstract = "Let $ p \geq 1 $, $ \varepsilon > 0 $, $ r \geq (1 + \varepsilon) p $, and $X$ be a $ ( - 1 / r)$-concave random vector in $ \mathbb {R}^n$ with Euclidean norm $ |X|$. We prove that\par $$ (\mathbb {E} |X|^p)^{1 / {p}} \leq c \left (C(\varepsilon) \mathbb {E} |X| + \sigma_p(X) \right), $$ where\par $$ \sigma_p(X) = \sup_{|z| \leq 1}(\mathbb {E} | \langle z, X \rangle |^p)^{1 / p}, $$ $ C(\varepsilon)$ depends only on $ \varepsilon $ and $c$ is a universal constant. Moreover, if in addition $X$ is centered then\par $$ (\mathbb {E} |X|^{-p})^{-1 / {p}} \geq c(\varepsilon) \left (\mathbb {E} |X| - C \sigma_p(X) \right) $$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "convex measures, $\kappa$-concave measure, tail inequalities, small ball probability estimate", } @Article{Conus:2012:CLB, author = "Daniel Conus and Mathew Joseph and Davar Khoshnevisan", title = "Correlation-length bounds, and estimates for intermittent islands in parabolic {SPDEs}", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "102:1--102:15", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2429", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2429", abstract = "We consider the nonlinear stochastic heat equation in one dimension. Under some conditions on the nonlinearity, we show that the ``peaks'' of the solution are rare, almost fractal like. We also provide an upper bound on the length of the ``islands'', the regions of large values. These results are obtained by analyzing the correlation length of the solution.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "intermittency; islands; peaks; The stochastic heat equation", } @Article{Barriere:2012:SRP, author = "Olivier Barri{\`e}re and Antoine Echelard and Jacques L{\'e}vy V{\'e}hel", title = "Self-regulating processes", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "103:1--103:30", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2010", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2010", abstract = "We construct functions and stochastic processes for which a functional relation holds between amplitude and local regularity, as measured by the pointwise or local H{\"o}lder exponent. We consider in particular functions and processes built by extending Weierstrass function, multifractional Brownian motion and the L{\'e}vy construction of Brownian motion. Such processes have recently proved to be relevant models in various applications. The aim of this work is to provide a theoretical background to these studies and to provide a first step in the development of a theory for such self-regulating processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "H{\"o}lder regularity; multifractional Brownian motion; self-regulating processes; Weierstrass function", } @Article{Gupta:2012:FVL, author = "Ankit Gupta", title = "The {Fleming--Viot} limit of an interacting spatial population with fast density regulation", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "104:1--104:55", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1964", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1964", abstract = "We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual is assigned a mass of $ 1 / N$ and the total mass in the system is called population density. The dynamics has an intrinsic density regulation mechanism that drives the population density towards an equilibrium. We show that under a timescale separation between the slow migration mechanism and the fast density regulation mechanism, the population dynamics converges to a Fleming--Viot process as the scaling parameter $ N \to \infty $. We first prove this result for a basic model in which the birth and death rates can only depend on the population density. In this case we obtain a neutral Fleming--Viot process. We then extend this model by including position-dependence in the birth and death rates, as well as, offspring dispersal and immigration mechanisms. We show how these extensions add mutation and selection to the limiting Fleming--Viot process. All the results are proved in a multi-type setting, where there are $q$ types of individuals reproducing each other. To illustrate the usefulness of our convergence result, we discuss certain applications in ecology and cell biology.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "carcinogenesis; cell polarity; density dependence; Fleming--Viot process; site fidelity; spatial population", } @Article{Bryc:2012:BQH, author = "W{\l}odek Bryc and Jacek Weso{\l}owski", title = "Bridges of quadratic harnesses", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "105:1--105:25", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1866", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1866", abstract = "Quadratic harnesses are typically non-homogeneous Markov processes with time-dependent state space. Motivated by a question raised in {\'E}mery and Yor (2004) we give explicit formulas for bridges of such processes. Using an appropriately defined f transformation we show that all bridges of a given quadratic harness can be transformed into other standard quadratic harnesses. Conversely, each such bridge is anf-transformation of a standard quadratic harness. We describe quadratic harnesses that correspond to bridges of some L{\'e}vy processes. We determine all quadratic harnesses that may arise from stitching together a pair of q-Meixner processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bridges; harnesses; L{\'e}vy-Meixner processes; quadratic conditional variances", } @Article{Aryasova:2012:PFG, author = "Olga Aryasova and Andrey Pilipenko", title = "On properties of a flow generated by an {SDE} with discontinuous drift", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "106:1--106:20", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-2138", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2138", abstract = "We consider a stochastic flow on $ \mathbb {R} $ generated by an SDE with its drift being a function of bounded variation. We show that the flow is differentiable with respect to the initial conditions. Asymptotic properties of the flow are studied.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "differentiability with respect to initial data; local times; stochastic flow", } @Article{Klimsiak:2012:RBM, author = "Tomasz Klimsiak", title = "Reflected {BSDEs} with monotone generator", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "107:1--107:25", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1759", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1759", abstract = "We give necessary and sufficient condition for existence and uniqueness of $ \mathbb {L}^p$-solutions of reflected BSDEs with continuous barrier, generator monotone with respect to $y$ and Lipschitz continuous with respect to $z$, and with data in $ \mathbb {L}^p$, $ p \ge 1$. We also prove that the solutions maybe approximated by the penalization method.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Lp-solutions; monotone generator; Reflected backward stochastic differential equation", } @Article{Heil:2013:SMP, author = "Hadrian Heil", title = "A stationary, mixing and perturbative counterexample to the $0$--$1$-law for random walk in random environment in two dimensions", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "1:1--1:33", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1880", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1880", abstract = "We construct a two-dimensional counterexample of a random walk in random environment (RWRE). The environment is stationary, mixing and perturbative, and the corresponding RWRE has non trivial probability to wander off to the upper right. This is in contrast to the 0-1-law that holds for i.i.d. environments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "0-1-Law; Counterexample; Random Walk in Random Environment", } @Article{Chen:2013:CLT, author = "Wei-Kuo Chen", title = "Central limit theorems for cavity and local fields of the {Sherrington--Kirkpatrick} model", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "2:1--2:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1763", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1763", abstract = "One of the remarkable applications of the cavity method in the mean field spin glasses is to prove the validity of the Thouless--Anderson--Palmer (TAP) system of equations in the Sherrington--Kirkpatrick (SK) model in the high temperature regime. This naturally leads us to the study of the limit laws for cavity and local fields. The first quantitative results for both fields were obtained by Chatterjee using Stein's method. In this paper, we approach these problems using the Gaussian interpolation technique and establish central limit theorems for both fields by giving moment estimates of all orders.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Sherrington--Kirkpatrick model; Stein's method; TAP equations", } @Article{Deya:2013:SHE, author = "Aur{\'e}lien Deya and Maria Jolis and Llu{\'\i}s Quer-Sardanyons", title = "The {Stratonovich} heat equation: a continuity result and weak approximations", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "3:1--3:34", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2004", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2004", abstract = "We consider a Stratonovich heat equation in $ (0, 1) $ with a nonlinear multiplicative noise driven by a trace-class Wiener process. First, the equation is shown to have a unique mild solution. Secondly, convolutional rough paths techniques are used to provide an almost sure continuity result for the solution with respect to the solution of the 'smooth' equation obtained by replacing the noise with an absolutely continuous process. This continuity result is then exploited to prove weak convergence results based on Donsker and Kac--Stroock type approximations of the noise.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "convergence in law; convolutional rough paths theory; stochastic heat equation; Stratonovich integral", } @Article{Rath:2013:ESQ, author = "Bal{\'a}zs R{\'a}th and Art{\"e}m Sapozhnikov", title = "The effect of small quenched noise on connectivity properties of random interlacements", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "4:1--4:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2122", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2122", abstract = "Random interlacements (at level $u$) is a one parameter family of random subsets of $ \mathbb {Z}^d$ introduced by Sznitman. The vacant set at level $u$ is the complement of the random interlacement at level $u$. While the random interlacement induces a connected subgraph of $ \mathbb {Z}^d$ for all levels $u$, the vacant set has a non-trivial phase transition in $u$.\par In this paper, we study the effect of small quenched noise on connectivity properties of the random interlacement and the vacant set. For a positive $ \varepsilon $, we allow each vertex of the random interlacement (referred to as occupied) to become vacant, and each vertex of the vacant set to become occupied with probability $ \varepsilon $, independently of the randomness of the interlacement, and independently for different vertices. We prove that for any $ d \geq 3$ and $ u > 0$, almost surely, the perturbed random interlacement percolates for small enough noise parameter $ \varepsilon $. In fact, we prove the stronger statement that Bernoulli percolation on the random interlacement graph has a non-trivial phase transition in wide enough slabs. As a byproduct, we show that any electric network with i.i.d. positive resistances on the interlacement graph is transient. As for the vacant set, we show that for any $ d \geq 3$, there is still a non trivial phase transition in $u$ when the noise parameter $ \varepsilon $ is small enough, and we give explicit upper and lower bounds on the value of the critical threshold, when $ \varepsilon \to 0$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bernoulli percolation; long-range correlations; quenched noise; Random interlacements; slab; transience; vacant set", } @Article{Alexander:2013:SCR, author = "Kenneth Alexander and Nikolaos Zygouras", title = "Subgaussian concentration and rates of convergence in directed polymers", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "5:1--5:28", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2005", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2005", abstract = "We consider directed random polymers in $ (d + 1) $ dimensions with nearly gamma i.i.d. disorder. We study the partition function $ Z_{N, \omega } $ and establish exponential concentration of $ \log Z_{N, \omega } $ about its mean on the subGaussian scale $ \sqrt {N / \log N} $. This is used to show that $ \mathbb {E}[\log Z_{N, \omega }] $ differs from $N$ times the free energy by an amount which is also subGaussian (i.e., $ o(\sqrt {N})$), specifically $ O(\sqrt {\frac {N}{\log N}} \log \log N)$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "directed polymers, concentration, modified Poincar{\'e} inequalities, coarse graining", } @Article{Bassetti:2013:SCE, author = "Federico Bassetti and Eleonora Perversi", title = "Speed of convergence to equilibrium in {Wasserstein} metrics for {Kac}-like kinetic equations", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "6:1--6:35", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2054", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2054", abstract = "This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the domain of normal attraction of an $ \alpha $-stable law, the solution of the equation converges weakly to a suitable scale mixture of centered $ \alpha $-stable laws. In this paper we present explicit exponential rates for the convergence to equilibrium in Kantorovich--Wasserstein distances of order $ p > \alpha $, under the natural assumption that the distance between the initial datum and the limit distribution is finite. For $ \alpha = 2$ this assumption reduces to the finiteness of the absolute moment of order $p$ of the initial datum. On the contrary, when $ \alpha < 2$, the situation is more problematic due to the fact that both the limit distribution and the initial datum have infinite absolute moment of any order $ p > \alpha $. For this case, we provide sufficient conditions for the finiteness of the Kantorovich--Wasserstein distance.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Boltzmann-like equations, Kac caricature, smoothing transformation, stable laws, rate of convergence to equilibrium, Wasserstein distances", } @Article{Dombry:2013:RCD, author = "Cl{\'e}ment Dombry and Fr{\'e}d{\'e}ric Eyi-Minko", title = "Regular conditional distributions of continuous max-infinitely divisible random fields", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "7:1--7:21", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1991", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1991", abstract = "This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $ \{ \eta (t) \}_{t \in T} $ given observations $ \{ \eta (t_i) = y_i, \ 1 \leq i \leq k \} $. Our starting point is the point process representation of max-infinitely divisible processes by Gin{\'e}, Hahn and Vatan (1990). We carefully analyze the structure of the underlying point process, introduce the notions of extremal function, sub-extremal function and hitting scenario associated to the constraints and derive the associated distributions. This allows us to explicit the conditional distribution as a mixture over all hitting scenarios compatible with the conditioning constraints. This formula extends a recent result by Wang and Stoev (2011) dealing with the case of spectrally discrete max-stable random fields. This paper offers new tools and perspective or prediction in extreme value theory together with numerous potential applications.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "max-infinitely divisible process; max-stable process; point process representation; regular conditional distribution", } @Article{Jordan:2013:GPA, author = "Jonathan Jordan", title = "Geometric preferential attachment in non-uniform metric spaces", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "8:1--8:15", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2271", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2271", abstract = "We investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that of the preferential attachment with multiplicative fitness models investigated by Borgs et al. When the metric space is finite, the degree distribution at each point of the space converges to a degree distribution which is an asymptotic power law whose index depends on the chosen point. For infinite metric spaces, we can show that for vertices in a Borel subset of $S$ of positive measure the degree distribution converges to a distribution whose tail is close to that of a power law whose index again depends on the set.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "geometric random graphs; preferential attachment", } @Article{Lin:2013:SDE, author = "Yiqing Lin", title = "Stochastic differential equations driven by {$G$}-{Brownian} motion with reflecting boundary conditions", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "9:1--9:23", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2566", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2566", abstract = "In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the $G$-framework and extend $G$-It{\^o}'s formula. Moreover, we study the solvability of the scalar valued stochastic differential equations driven by $G$ Brownian motion with reflecting boundary conditions (RGSDEs).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$G$-Brownian motion; $G$-expectation; $G$-It{\^o}'s formula; $G$-stochastic differential equations; increasing processes; reflecting boundary conditions", } @Article{Bardet:2013:TVE, author = "Jean-Baptiste Bardet and Alejandra Christen and Arnaud Guillin and Florent Malrieu and Pierre-Andr{\'e} Zitt", title = "Total variation estimates for the {TCP} process", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "10:1--10:21", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1720", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1720", abstract = "The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet. This continuous time Markov process takes its values in $ [0, \infty) $, is ergodic and irreversible. The sample paths are piecewise linear deterministic and the whole randomness of the dynamics comes from the jump mechanism. The aim of the present paper is to provide quantitative estimates for the exponential convergence to equilibrium, in terms of the total variation and Wasserstein distances.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Additive Increase Multiplicative Decrease Processes (AIMD); Coupling; Exponential Ergodicity; Network Protocols; Piecewise Deterministic Markov Processes (PDMP); Queueing Theory", } @Article{Shkolnikov:2013:SUE, author = "Mykhaylo Shkolnikov", title = "Some universal estimates for reversible {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "11:1--11:17", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1749", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1749", abstract = "We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the $ L^2 $ norms. The estimates in total variation norm are obtained using a novel identity relating the convergence to equilibrium of a reversible Markov chain to the increase in the entropy of its one-dimensional distributions. In addition, we propose a universal way of defining the ultrametric partition structure on the state space of such Markov chains. Finally, for chains reversible with respect to the uniform measure, we show how the global convergence to equilibrium can be controlled using the entropy accumulated by the chain.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "convergence to equilibrium; entropy; Reversible Markov chains; time of coupling", } @Article{Dawson:2013:PUS, author = "Donald Dawson and Luis Gorostiza", title = "Percolation in an ultrametric space", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "12:1--12:26", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1789", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1789", abstract = "We study percolation in the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $ c_k / N^{k(1 + \delta)}, \delta > - 1 $. Since the distance is an ultrametric, there are significant differences with percolation in the Euclidean lattice. We consider three regimes: $ \delta < 1$, where percolation occurs, $ \delta > 1$, where it does not occur, and $ \delta = 1$ which is the critical case corresponding to the phase transition. In the critical case we use an approach in the spirit of the renormalization group method of statistical physics, and connectivity results of Erd{\H{o}}s--R{\'e}nyi random graphs play a key role. We find sufficient conditions on $ c_k$ such that percolation occurs, or that it does not occur. An intermediate situation called pre-percolation, which is necessary for percolation, is also considered. In the cases of percolation we prove uniqueness of the constructed percolation clusters. In a previous paper we studied percolation in the $ N \to \infty $ limit (mean field percolation), which provided a simplification that allowed finding a necessary and sufficient condition for percolation. For fixed $N$ there are open questions, in particular regarding the behaviour at the critical values of parameters in the definition of $ c_k$. Those questions suggest the need to study {\em ultrametric random graphs}.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "hierarchical graph; Percolation; renormalization; ultrametric", } @Article{Lopker:2013:TRP, author = "Andreas L{\"o}pker and Zbigniew Palmowski", title = "On time reversal of piecewise deterministic {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "13:1--13:29", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1958", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1958", abstract = "We study the time reversal of a general Piecewise Deterministic Markov Process (PDMP). The time reversed process is defined as $ X_{(T - t)-} $, where $T$ is some given time and $ X_t$ is a stationary PDMP. We obtain the parameters of the reversed process, like the jump intensity and the jump measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Piecewise Deterministic Markov Processes, time reversal, Stationary distribution", } @Article{Abraham:2013:NGH, author = "Romain Abraham and Jean-Fran{\c{c}}ois Delmas and Patrick Hoscheit", title = "A note on the {Gromov--Hausdorff--Prokhorov} distance between (locally) compact metric measure spaces", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "14:1--14:21", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2116", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2116", abstract = "We present an extension of the Gromov--Hausdorff metric on the set of compact metric spaces: the Gromov--Hausdorff--Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a boundedly finite measure. We prove that this space with the extended Gromov--Hausdorff--Prokhorov metric is a Polish space. This generalization is needed to define L{\'e}vy trees, which are (possibly unbounded) random real trees endowed with a boundedly finite measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "boundedly finite measure; Gromov--Hausdorff; length space; L{\'e}vy tree; Prokhorov metric", } @Article{Tan:2013:SMF, author = "Xiaolu Tan", title = "A splitting method for fully nonlinear degenerate parabolic {PDEs}", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "15:1--15:24", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1967", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1967", abstract = "Motivated by applications in Asian option pricing, optimal commodity trading etc., we propose a splitting scheme for a fully nonlinear degenerate parabolic PDEs. The splitting scheme generalizes the probabilistic scheme of Fahim, Touzi and Warin to the degenerate case. We also provide a simulation-regression method to make the splitting scheme implementable. General convergence as well as rate of convergence are obtained under reasonable conditions. Finally, we give some numerical tests in an Asian option pricing problem and an optimal hydropower management problem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "nonlinear degenerate PDE; Numerical scheme; splitting method; viscosity solution", } @Article{Hwang:2013:ECL, author = "Hsien-Kuei Hwang and Svante Janson", title = "Erratum: {``A central limit theorem for random ordered factorizations of integers''}", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "16:1--16:3", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2297", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Hwang:2011:CLT}.", URL = "http://ejp.ejpecp.org/article/view/2297", abstract = "This is an erratum for {\bf \url{https://doi.org/10.1214/EJP.v16-858} EJP volume {\bf 16} paper 12}.\par We fix a gap in the proof of our estimates for odd moments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Tauberian theorems, Ordered factorizations, central limit theorem, method of moments, Dirichlet series", } @Article{Friesen:2013:PTL, author = "Olga Friesen and Matthias L{\"o}we", title = "A phase transition for the limiting spectral density of random matrices", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "17:1--17:17", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2118", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2118", abstract = "We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated. Depending on the strength of correlation, the limiting spectral distribution is either the famous semicircle distribution, the distribution derived for Toeplitz matrices by Bryc, Dembo and Jiang (2006), or the free convolution of the two distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random matrices, dependent random variables, Toeplitz matrices, semicircle law, Curie--Weiss model", } @Article{Devulder:2013:RWR, author = "Alexis Devulder and Fran{\c{c}}oise P{\`e}ne", title = "Random walk in random environment in a two-dimensional stratified medium with orientations", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "18:1--18:23", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2459", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2459", abstract = "We consider a model of random walk in $ {\mathbb Z}^2 $ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed orientations under general hypotheses. This contrasts with the model of Campanino and Petritis, in which probabilities to stay on these lines are all equal. We also establish a result of convergence in distribution for this walk with suitable normalizations under more precise assumptions. In particular, our model proves to be, in many cases, even more superdiffusive than the random walks introduced by Campanino and Petritis.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "functional limit theorem; random walk in random environment; random walk in random scenery; random walk on randomly oriented lattices; transience", } @Article{Alberts:2013:NCS, author = "Tom Alberts and Marcel Ortgiese", title = "The near-critical scaling window for directed polymers on disordered trees", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "19:1--19:24", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2036", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2036", abstract = "We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on the asymptotics of the partition function in the near-critical regime, where the inverse temperature is a small perturbation away from the critical one with the perturbation converging to zero as the system size grows large. Depending on the speed of convergence we observe very different asymptotic behavior. If the perturbation is small then we are inside the critical window and observe the same decay of the partition function as at the critical temperature. If the perturbation is slightly larger the near critical scaling leads to a new range of asymptotic behaviors, which at the extremes match up with the already known rates for the sub- and super-critical regimes. We use our results to identify the size of the fluctuations of the typical energies under the critical Gibbs measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Directed polymers in random environment, branching random walk, multiplicative cascades, critical temperature, near critical scaling", } @Article{Subag:2013:LBM, author = "Eliran Subag", title = "A lower bound for the mixing time of the random-to-random Insertions shuffle", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "20:1--20:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1950", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1950", abstract = "The best known lower and upper bounds on the mixing time for the random to-random insertions shuffle are $ (1 / 2 - o(1))n \log n $ and $ (2 + o(1))n \log n $. A long standing open problem is to prove that the mixing time exhibits a cutoff. In particular, Diaconis conjectured that the cutoff occurs at $ 3 / 4 n \log n $. Our main result is a lower bound of $ t_n = (3 / 4 - o(1))n \log n $, corresponding to this conjecture. Our method is based on analysis of the positions of cards yet-to-be removed. We show that for large $n$ and $ t_n$ as above, there exists $ f(n) = \Theta (\sqrt {n \log n})$ such that, with high probability, under both the measure induced by the shuffle and the stationary measure, the number of cards within a certain distance from their initial position is $ f(n)$ plus a lower order term. However, under the induced measure, this lower order term is strongly influenced by the number of cards yet-to-be-removed, and is of higher order than for the stationary measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Mixing-time, card shuffling, random insertions, cutoff phenomenon", } @Article{Sarkar:2013:BWS, author = "Anish Sarkar and Rongfeng Sun", title = "{Brownian} web in the scaling limit of supercritical oriented percolation in dimension $ 1 + 1 $", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "21:1--21:23", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2019", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2019", abstract = "We prove that, after centering and diffusively rescaling space and time, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice $ Z^2_{\rm even} := \{ (x, i) \in Z^2 \} $: $ x + i $ even, converges in distribution to the Brownian web. This proves a conjecture of Wu and Zhang. Our key observation is that each rightmost infinite open path can be approximated by a percolation exploration cluster, and different exploration clusters evolve independently before they intersect.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian web; oriented percolation", } @Article{Nourdin:2013:ACC, author = "Ivan Nourdin and David Nualart and Guillaume Poly", title = "Absolute continuity and convergence of densities for random vectors on {Wiener} chaos", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "22:1--22:19", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2181", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2181", abstract = "The aim of this paper is to establish some new results on the absolute continuity and the convergence in total variation for a sequence of d-dimensional vectors whose components belong to a finite sum of Wiener chaoses. First we show that the probability that the determinant of the Malliavin matrix of such vectors vanishes is zero or one, and this probability equals to one is equivalent to say that the vector takes values in the set of zeros of a polynomial. We provide a bound for the degree of this annihilating polynomial improving a result by Kusuoka. On the other hand, we show that the convergence in law implies the convergence in total variation, extending to the multivariate case a recent result by Nourdin and Poly. This follows from an inequality relating the total variation distance with the Fortet-Mourier distance. Finally, applications to some particular cases are discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Convergence in distribution; Convergence in total variation; Malliavin calculus; multiple Wiener--It{\^o} integral; Wiener chaos", } @Article{Foucart:2013:SCS, author = "Cl{\'e}ment Foucart and Olivier H{\'e}nard", title = "Stable continuous-state branching processes with immigration and Beta-{Fleming--Viot} processes with immigration", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "23:1--23:21", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2024", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2024", abstract = "Branching processes and Fleming--Viot processes are two main models in stochastic population theory. Incorporating an immigration in both models, we generalize the results of Shiga (1990) and Birkner (2005) which respectively connect the Feller diffusion with the classical Fleming--Viot process and the $ \alpha $-stable continuous state branching process with the $ B e t a(2 - \alpha, \alpha)$-generalized Fleming--Viot process. In a recent work, a new class of probability-measure valued processes, called $M$-generalized Fleming--Viot processes with immigration, has been set up in duality with the so-called $M$ coalescents. The purpose of this article is to investigate the links between this new class of processes and the continuous-state branching processes with immigration. In the specific case of the $ \alpha $-stable branching process conditioned to be never extinct, we get that its genealogy is given, up to a random time change, by a $ B e t a(2 - \alpha, \alpha - 1)$-coalescent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Measure-valued processes, Continuous-state branching processes, Fleming--Viot processes, Immigration, Beta-Coalescent, Generators, Random time change", } @Article{Berglund:2013:SEM, author = "Nils Berglund and Barbara Gentz", title = "Sharp estimates for metastable lifetimes in parabolic {SPDEs}: {Kramers}' law and beyond", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "24:1--24:58", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1802", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1802", abstract = "We prove a Kramers-type law for metastable transition times for a class of one-dimensional parabolic stochastic partial differential equations (SPDEs) with bistable potential. The expected transition time between local minima of the potential energy depends exponentially on the energy barrier to overcome, with an explicit prefactor related to functional determinants. Our results cover situations where the functional determinants vanish owing to a bifurcation, thereby rigorously proving the results of formal computations announced in a previous work. The proofs rely on a spectral Galerkin approximation of the SPDE by a finite-dimensional system, and on a potential-theoretic approach to the computation of transition times in finite dimension.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "capacities; exit problem; Galerkin approximation; Kramers' law; large deviations; metastability; pitchfork bifurcation; potential theory; reaction-diffusion equations; SPDEs; subexponential asymptotics; transition time; Wentzell--Freidlin theory", } @Article{Barden:2013:CLT, author = "Dennis Barden and Huiling Le and Megan Owen", title = "Central limit theorems for {Fr{\'e}chet} means in the space of phylogenetic trees", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "25:1--25:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2201", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2201", abstract = "This paper studies the characterisation, and the limiting distributions, of Fr{\'e}chet means in the space of phylogenetic trees. This space is topologically stratified, as well as being a CAT(0) space. We use a generalised version of the Delta method to demonstrate non-classical behaviour arising from the global topological structure of the space. In particular, we show that, for the space of trees with four leaves, although they are related to the Gaussian distribution, the forms taken by the limiting distributions depend on the co-dimensions of the strata in which the Fr{\'e}chet means lie.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "central limit theorem; Frechet mean; phylogenetic trees; stratified manifold", } @Article{Cetin:2013:PPB, author = "Umut Cetin and Hao Xing", title = "Point process bridges and weak convergence of insider trading models", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "26:1--26:24", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2039", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2039", abstract = "We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time $1$ value satisfies a specific constraint. This construction allows us to show the existence of Glosten--Milgrom equilibrium and its associated optimal trading strategy for the insider. In the equilibrium the insider employs a mixed strategy to randomly submit two types of orders: one type trades in the same direction as noise trades while the other cancels some of the noise trades by submitting opposite orders when noise trades arrive. The construction also allows us to prove that Glosten--Milgrom equilibria converge weakly to Kyle-Back equilibrium, without the additional assumptions imposed in {\em K. Back and S. Baruch, Econometrica, 72 (2004), pp. 433-465}, when the common intensity of the Poisson processes tends to infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "point process bridge, Glosten--Milgrom model, Kyle model, insider trading, equilibrium, weak convergence", } @Article{Bartroff:2013:BEB, author = "Jay Bartroff and Larry Goldstein", title = "A {Berry--Ess{\'e}en} bound for the uniform multinomial occupancy model", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "27:1--27:29", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1983", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1983", abstract = "The inductive size bias coupling technique and Stein's method yield a {Berry--Ess{\'e}en} theorem for the number of urns having occupancy $ d \geq 2 $ when $n$ balls are uniformly distributed over $m$ urns. In particular, there exists a constant $C$ depending only on $d$ such that\par $$ \sup_{z \in \mathbb {R}} \left |P \left (W_{n, m} \leq z \right) - P(Z \leq z) \right | \le C \frac {\sigma_{n, m}}{1 + (\frac {n}{m})^3} \quad \mbox {for all $ n \ge d$ a n d $ m \ge 2$, } $$ \par where $ W_{n, m}$ and $ \sigma_{n, m}^2$ are the standardized count and variance, respectively, of the number of urns with $d$ balls, and $Z$ is a standard normal random variable. Asymptotically, the bound is optimal up to constants if $n$ and $m$ tend to infinity together in a way such that $ n / m$ stays bounded.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coupling; size bias; Stein's method; urn models", } @Article{Pinsky:2013:DTR, author = "Ross Pinsky", title = "Detecting tampering in a random hypercube", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "28:1--28:12", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2290", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2290", abstract = "Consider the random hypercube $ H_2^n(p_n) $ obtained from the hypercube $ H_2^n $ by deleting any given edge with probability $ 1 - p_n $, independently of all the other edges. A diameter path in $ H_2^n $ is a longest geodesic path in $ H_2^n $. Consider the following two ways of tampering with the random graph $ H_2^n(p_n) $: (i) choose a diameter path at random and adjoin all of its edges to $ H_2^n(p_n) $; (ii) choose a diameter path at random from among those that start at $ 0 = (0, \cdots, 0) $, and adjoin all of its edges to $ H_2^n(p_n) $. We study the question of whether these tamperings are detectable asymptotically as $ n \to \infty $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random graph, random hypercube, total variation norm, detection", } @Article{Schuett:2013:ENR, author = "Carsten Schuett and Stiene Riemer", title = "On the expectation of the norm of random matrices with non-identically distributed entries", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "29:1--29:13", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2103", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2103", abstract = "Let $ X_{i, j} $, $ i, j = 1, \ldots {}, n $, be independent, not necessarily identically distributed random variables with finite first moments. We show that the norm of the random matrix $ (X_{i, j})_{i, j = 1}^n $ is up to a logarithmic factor of the order of $ \mathbb {E} \max \limits_{i = 1, \ldots {}, n} \left \Vert (X_{i, j})_{j = 1}^n \right \Vert_2 + \mathbb {E} \max \limits_{i = 1, \ldots {}, n} \left \Vert (X_{i, j})_{j = 1}^n \right \Vert_2 $. This extends (and improves in most cases) the previous results of Seginer and Latala.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Largest Singular Value; Orlicz Norm; Random Matrix", } @Article{Campi:2013:ECD, author = "Luciano Campi and Umut Cetin and Albina Danilova", title = "Explicit construction of a dynamic {Bessel} bridge of dimension $3$", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "30:1--30:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1907", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1907", abstract = "Given a deterministically time-changed Brownian motion $Z$ starting from $1$, whose time-change $ V(t)$ satisfies $ V(t) > t$ for all $ t > 0$, we perform an explicit construction of a process $X$ which is Brownian motion in its own filtration and that hits zero for the first time at $ V(\tau)$, where $ \tau := \inf \{ t > 0 \colon Z_t = 0 \} $. We also provide the semimartingale decomposition of $X$ under the filtration jointly generated by $X$ and $Z$. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process $X$ may be viewed as the analogue of a $3$-dimensional Bessel bridge starting from $1$ at time $0$ and ending at $0$ at the random time $ V(\tau)$. We call this a {\em dynamic Bessel bridge} since $ V(\tau)$ is not known in advance. Our study is motivated by insider trading models with default risk, where the insider observes the firm's value continuously on time. The financial application, which uses results proved in the present paper, has been developed in a companion paper.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "credit risk; Dynamic Bessel bridge; enlargement of filtrations; filtering insider trading", } @Article{Ganguly:2013:WZT, author = "Arnab Ganguly", title = "{Wong--Zakai} type convergence in infinite dimensions", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "31:1--31:34", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2650", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2650", abstract = "The paper deals with convergence of solutions of a class of stochastic differential equations driven by infinite-dimensional semimartingales. The infinite dimensional semimartingales considered in the paper are Hilbert-space valued. The theorems presented generalize the convergence result obtained by Wong and Zakai for stochastic differential equations driven by linear interpolations of a finite-dimensional Brownian motion. In particular, a general form of the correction factor is derived. Examples are given illustrating the use of the theorems to obtain other kinds of approximation results.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$H^{\#}$-semimartingales; Banach space-valued semimartingales; infinite-dimensional semimartingales; stochastic differential equation; Weak convergence; Wong--Zakai, uniform tightness", } @Article{Lachieze-Rey:2013:FGF, author = "Raphael Lachieze-Rey and Giovanni Peccati", title = "Fine {Gaussian} fluctuations on the {Poisson} space, {I}: contractions, cumulants and geometric random graphs", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "32:1--32:32", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2104", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2104", abstract = "We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit theorems. These conditions can always be expressed in terms of contraction operators or, equivalently, fourth cumulants. Our findings are specifically tailored to deal with the normal approximation of the geometric $U$-statistics introduced by Reitzner and Schulte (2011). In particular, we shall provide a new analytic characterization of geometric random graphs whose edge-counting statistics exhibit asymptotic Gaussian fluctuations, and describe a new form of Poisson convergence for stationary random graphs with sparse connections. In a companion paper, the above analysis is extended to general $U$-statistics of marked point processes with possibly rescaled kernels.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$U$-statistics; Central Limit Theorems; Contractions; Malliavin Calculus; Poisson Limit Theorems; Poisson Space; Random Graphs; Stein's Method; Wasserstein Distance; Wiener Chaos", } @Article{Ezanno:2013:SRA, author = "Fran{\c{c}}ois Ezanno", title = "Some results about ergodicity in shape for a crystal growth model", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "33:1--33:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2177", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2177", abstract = "We study a crystal growth Markov model proposed by Gates and Westcott. This is an aggregation process where particles are packed in a square lattice accordingly to prescribed deposition rates. This model is parametrized by three values $ (\beta_i, i = 0, 1, 2) $ corresponding to depositions on three different types of sites. The main problem is to determine, for the shape of the crystal, when recurrence and when ergodicity do occur. Sufficient conditions are known both for ergodicity and transience. We establish some improved conditions and give a precise description of the asymptotic behavior in a special case.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Markov chain; positive recurrence; random deposition", } @Article{Lamberton:2013:OSO, author = "Damien Lamberton and Mihail Zervos", title = "On the optimal stopping of a one-dimensional diffusion", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "34:1--34:49", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2182", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2182", abstract = "We consider the one-dimensional diffusion $X$ that satisfies the stochastic differential equation\par $$ d X_t = b(X_t) \, d t + \sigma (X_t) \, d W_t $$ in the interior $ {\rm int}(I) =] \alpha, \beta [$ of a given interval $ I \subseteq [ - \infty, \infty]$, where $ b, \sigma \colon \int (I) \rightarrow \mathbb {R}$ are Borel-measurable functions and $W$ is a standard one-dimensional Brownian motion. We allow for the endpoints $ \alpha $ and $ \beta $ to be inaccessible or absorbing.\par Given a Borel-measurable function $ r \colon I \rightarrow \mathbb {R}_+$ that is uniformly bounded away from 0, we establish a new analytic representation of the $ r(\cdot)$ potential of a continuous additive functional of $X$. Furthermore, we derive a complete characterisation of differences of two convex functions in terms of appropriate $ r(\cdot)$-potentials, and we show that a function $ F \colon I \rightarrow \mathbb {R}_+$ is $ r(\cdot)$-excessive if and only if it is the difference of two convex functions and $ - \bigl (\frac {1}{2} \sigma^2 F'' + b F' - r F \bigr)$ is a positive measure. We use these results to study the optimal stopping problem that aims at maximising the performance index\par $$ \mathbb {E}_x \left [\exp \left ( - \int_0^\tau r(X_t) \, d t \right) f(X_\tau) \\ {\bf 1}_{\{ \tau < \infty \} } \right] $$ over all stopping times $ \tau $, where $ f \colon I \rightarrow \mathbb {R}_+$ is a Borel-measurable function that may be unbounded. We derive a simple necessary and sufficient condition for the value function $v$ of this problem to be real valued. In the presence of this condition, we show that $v$ is the difference of two convex functions, and we prove that it satisfies the variational inequality\par $$ \max \left \{ \frac {1}{2} \sigma^2 v'' + b v' - r v, \ \overline {f} - v \right \} = 0 $$ in the sense of distributions, where $ \overline {f}$ identifies wit the upper semicontinuous envelope of $f$ in the interior $ i n t(I)$ of $I$. Conversely, we derive a simple necessary and sufficient condition for a solution to the equation above to identify with the value function $v$. Furthermore, we establish several other characterisations of the solution to the optimal stopping problem, including a generalisation of the so-called ``principle of smooth fit''. In our analysis, we also make a construction that is concerned with pasting weak solutions to the SDE at appropriate hitting times, which is an issue of fundamental importance to dynamic programming.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "additive functionals; one-dimensional diffusions; optimal stopping; potentials; variational inequalities", } @Article{Levin:2013:CLT, author = "Mordechay Levin", title = "{Central Limit Theorem} for {$ \mathbb {Z}_+^d $}-actions by toral endomorphisms", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "35:1--35:42", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1904", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1904", abstract = "In this paper we prove the central limit theorem for the following multisequence\par $$ \sum_{n_1 = 1}^{N_1} \ldots {} \sum_{n_d = 1}^{N_d} f(A_1^{n_1} \ldots {}A_d^{n_d} {\bf x}) $$ where $f$ is a H{\"o}lder's continue function, $ A_1, \ldots, A_d$ are $ s \times s$ partially hyperbolic commuting integer matrices, and $ \bf x$ is a uniformly distributed random variable in $ [0, 1]^s$. Next we prove the functional central limit theorem, and the almost sure central limit theorem. The main tool is the $S$-unit theorem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Central limit theorem, partially hyperbolic actions, toral endomorphisms", } @Article{Werner:2013:CS, author = "Wendelin Werner and Hao Wu", title = "From CLE({$ \kappa $}) to SLE({$ \kappa, \rho $})'s", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "36:1--36:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2376", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2376", abstract = "We show how to connect together the loops of a simple Conformal Loop Ensemble (CLE) in order to construct samples of chordal SLE$_{\kappa }$ processes and their SLE$_{\kappa }(\rho)$ variants, and we discuss some consequences of this construction.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "CLE; Conformal restriction; Hausdorff dimension; SLE", } @Article{Delmas:2013:WDS, author = "Jean-Fran{\c{c}}ois Delmas and Olivier H{\'e}nard", title = "A {Williams} decomposition for spatially dependent superprocesses", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "37:1--37:43", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1801", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1801", abstract = "We present a genealogy for superprocesses with a non-homogeneous quadratic branching mechanism, relying on a weighted version of the superprocess introduced by Engl{\"a}nder and Pinsky and a Girsanov theorem. We then decompose this genealogy with respect to the last individual alive (Williams' decomposition). Letting the extinction time tend to infinity, we get the Q-process by looking at the superprocess from the root, and define another process by looking from the top. Examples including the multitype Feller diffusion (investigated by Champagnat and Roelly) and the superdiffusion are provided.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Spatially dependent superprocess, Williams' decomposition, genealogy, h-transform, Q-process", } @Article{Bloznelis:2013:ACS, author = "Mindaugas Bloznelis and Jerzy Jaworski and Valentas Kurauskas", title = "Assortativity and clustering of sparse random intersection graphs", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "38:1--38:24", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2277", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2277", abstract = "We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of adjacent nodes (called the assortativity coefficient), the expected number of common neighbours of adjacent nodes, and the expected degree of a neighbour of a node of a given degree k. These expressions are written in terms of the asymptotic degree distribution and, alternatively, in terms of the parameters defining the underlying random graph model.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "assortativity; clustering; power law; random graph; random intersection graph", } @Article{Zhang:2013:HDL, author = "Liang Zhang", title = "{Hausdorff} dimension of limsup random fractals", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "39:1--39:26", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2273", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2273", abstract = "In this paper we find a critical condition for nonempty intersection of a limsup random fractal and an independent fractal percolation set defined on the boundary of a spherically symmetric tree. We then use a codimension argument to derive a formula for the Hausdorff dimension of limsup random fractals.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Hausdorff dimension; Limsup random fractals", } @Article{Dhersin:2013:EBC, author = "Jean-St{\'e}phane Dhersin and Martin M{\"o}hle", title = "On the external branches of coalescents with multiple collisions", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "40:1--40:11", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2286", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2286", abstract = "A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (Lambda-coalescents) is provided. This recursion is used to derive asymptotic results as the sample size n tends to infinity for the joint moments of the external branch lengths and for the moments of the total external branch length of the Bolthausen--Sznitman coalescent. These asymptotic results are based on a differential equation approach, which is as well useful to obtain exact solutions for the joint moments of the external branch lengths for the Bolthausen--Sznitman coalescent. The results for example show that the lengths of two randomly chosen external branches are positively correlated for the Bolthausen--Sznitman coalescent, whereas they are negatively correlated for the Kingman coalescent provided that n > = 4.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Asymptotic expansions; Bolthausen--Sznitman coalescent; external branches; joint moments; Kingman coalescent; multiple collisions", } @Article{Doumas:2013:ARM, author = "Aristides Doumas and Vassilis Papanicolaou", title = "Asymptotics of the rising moments for the coupon collector's problem", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "41:1--41:15", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1746", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1746", abstract = "We develop techniques of computing the asymptotics of the moments of the number $ T_N $ of coupons that a collector has to buy in order to find all $N$ existing different coupons as $ N \rightarrow \infty $. The probabilities (occurring frequencies) of the coupons can be quite arbitrary. After mentioning the case where the coupon probabilities are equal we consider the general case (of unequal probabilities). For a large class of distributions (after adopting a dichotomy) we arrive at the leading behavior of the moments of $ T_N$ as $ N \rightarrow \infty $. We also present various illustrative examples.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Coupon collector's problem, higher asymptotics", } @Article{Kondratiev:2013:SGG, author = "Yuri Kondratiev and Tobias Kuna and Natascha Ohlerich", title = "Spectral gap for {Glauber} type dynamics for a special class of potentials", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "42:1--42:18", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2260", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2260", abstract = "We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on $ \mathbb {R}^d $. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carr{\'e} du champ'' and ``second carr{\'e} du champ'' for the associate infinitesimal generators $L$ are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of $L$ are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "absence of phase transition; Birth-and-death process; continuous system; Glauber dynamics; spectral gap", } @Article{Keller-Ressel:2013:RAP, author = "Martin Keller-Ressel and Walter Schachermayer and Josef Teichmann", title = "Regularity of affine processes on general state spaces", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "43:1--43:17", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2043", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2043", abstract = "We consider a stochastically continuous, affine Markov process in the sense of Duffie, Filipovic and Schachermayer, with c{\`a}dl{\`a}g paths, on a general state space D, i.e., an arbitrary Borel subset of $ R^d $. We show that such a process is always regular, meaning that its Fourier--Laplace transform is differentiable in time, with derivatives that are continuous in the transform variable. As a consequence, we show that generalized Riccati equations and L{\'e}vy--Khintchine parameters for the process can be derived, as in the case of $ D = R_+^m \times R^n $ studied in Duffie, Filipovic and Schachermayer (2003). Moreover, we show that when the killing rate is zero, the affine process is a semi -martingale with absolutely continuous characteristics up to its time of explosion. Our results generalize the results of Keller-Ressel, Schachermayer and Teichmann (2011) for the state space $ R_+^m \times R^n $ and provide a new probabilistic approach to regularity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "affine process, regularity, semimartingale, generalized Riccati equation", } @Article{Cimasoni:2013:CTI, author = "David Cimasoni and Hugo Duminil-Copin", title = "The critical temperature for the {Ising} model on planar doubly periodic graphs", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "44:1--44:18", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2352", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2352", abstract = "We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse temperature $ \beta $ for a graph $G$ with coupling constants $ (J_e)_{e \in E(G)}$ is obtained as the unique solution of an algebraic equation in the variables $ (\tanh (\beta J_e))_{e \in E(G)}$. This is achieved by studying the high-temperature expansion of the model using Kac--Ward matrices.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "critical temperature; Harnack curves; Ising model; Kac--Ward matrices; weighted periodic graph", } @Article{Bielecki:2013:IDB, author = "Tomasz Bielecki and Jacek Jakubowski and Mariusz Niew{\k{e}}g{\l}owski", title = "Intricacies of dependence between components of multivariate {Markov} chains: weak {Markov} consistency and weak {Markov} copulae", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "45:1--45:21", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2238", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2238", abstract = "In this paper we examine the problem of existence and construction of multivariate Markov chains such that their components are Markov chains with given laws. Specifically, we provide sufficient and necessary conditions, in terms of semimartingale characteristics, for a component of a multivariate Markov chain to be a Markov chain in its own filtration --- a property called weak Markov consistency. Accordingly, we introduce and discuss the concept of weak Markov copulae. Finally, we examine relationship between the concepts of weak Markov consistency and weak Markov copulae, and the corresponding strong versions of these concepts.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "compensator of random measure; dependence; marginal law; Markov consistency; Markov copulae.; Multivariate Markov chain", } @Article{Groeneboom:2013:EVL, author = "Piet Groeneboom", title = "Erratum: {``Vertices of the least concave majorant of Brownian motion with parabolic drift''}", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "46:1--46:1", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2697", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Groeneboom:2011:VLC}.", URL = "http://ejp.ejpecp.org/article/view/2697", abstract = "This corrects the scaling of (2.9) in {\bf \url{https://doi.org/10.1214/EJP.v16-959} EJP volume {\bf 16} paper 84 (2011)}.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Airy functions; Brownian motion, parabolic drift; concave majorant; Grenander estimate; jump processes; number of vertices", } @Article{Aldous:2013:FMW, author = "David Aldous and Mykhaylo Shkolnikov", title = "Fluctuations of martingales and winning probabilities of game contestants", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "47:1--47:17", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2422", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2422", abstract = "Within a contest there is some probability $ M_i(t) $ that contestant $i$ will be the winner, given information available at time $t$, and $ M_i(t)$ must be a martingale in $t$. Assume continuous paths, to capture the idea that relevant information is acquired slowly. Provided each contestant's initial winning probability is at most b, one can easily calculate, without needing further model specification, the expectations of the random variables $ N_b$ = number of contestants whose winning probability ever exceeds $b$, and $ D_{ab} = $ total number of down-crossings of the martingales over an interval $ [a, b]$. The distributions of $ N_b$ and $ D_{ab}$ do depend on further model details, and we study how concentrated or spread out the distributions can be. The extremal models for $ N_b$ correspond to two contrasting intuitively natural methods for determining a winner: progressively shorten a list of remaining candidates, or sequentially examine candidates to be declared winner or eliminated. We give less precise bounds on the variability of $ D_{ab}$. We formalize the setting of infinitely many contestants each with infinitesimally small chance of winning, in which the explicit results are more elegant. A canonical process in this setting is the Wright--Fisher diffusion associated with an infinite population of initially distinct alleles; we show how this process fits our setting and raise the problem of finding the distributions of $ N_b$ and $ D_{ab}$ for this process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "entrance boundary, fluctuations, martingale; up-crossing; Wright--Fisher diffusion", } @Article{Neufeld:2013:SUV, author = "Ariel Neufeld and Marcel Nutz", title = "Superreplication under volatility uncertainty for measurable claims", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "48:1--48:14", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2358", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2358", abstract = "We establish the duality-formula for the superreplication price in a setting of volatility uncertainty which includes the example of ``random $G$-expectation''. In contrast to previous results, the contingent claim is not assumed to be quasi-continuous.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Nonlinear expectation; Superreplication; Volatility uncertainty", } @Article{Matsumoto:2013:CFZ, author = "Sho Matsumoto and Tomoyuki Shirai", title = "Correlation functions for zeros of a {Gaussian} power series and {Pfaffians}", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "49:1--49:18", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2545", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2545", abstract = "We show that the zeros of the random power series with i.i.d. real Gaussian coefficients form a Pfaffian point process. We also show that the product moments for absolute values and signatures of the power series can also be expressed by Pfaffians.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian power series; Pfaffian; point process; zeros", } @Article{Richou:2013:NES, author = "Adrien Richou and Federica Masiero", title = "A note on the existence of solutions to {Markovian} superquadratic {BSDEs} with an unbounded terminal condition", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "50:1--50:15", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2124", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2124", abstract = "In [Stochastc Process. Appl., 122(9):3173-3208], the author proved the existence and the uniqueness of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition when the generator and the terminal condition are locally Lipschitz. In this paper, we prove that the existence result remains true for these BSDEs when the regularity assumption on the terminal condition is weakened.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Backward stochastic differential equation; Existence result; Generator of superquadratic growth; Unbounded terminal condition", } @Article{Busic:2013:DCI, author = "Ana Bu{\v{s}}i{\'c} and Nazim Fat{\`e}s and Jean Mairesse and Ir{\`e}ne Marcovici", title = "Density classification on infinite lattices and trees", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "51:1--51:22", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2325", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2325", abstract = "Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter $p$. We address the density classification problem, that is, we want to design a (probabilistic or deterministic)cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether $p$ is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p < 1/2, and only 1's if p > 1/2. We present solutions to the problem on the regular grids of dimension d, for any d > 1, and on the regular infinite trees. For the bi-infinite line, we propose some candidates that weback up with numerical simulations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Cellular automata, interacting particle systems, density classification", } @Article{DaiPra:2013:EDI, author = "Paolo {Dai Pra} and Gustavo Posta", title = "Entropy decay for interacting systems via the {Bochner--Bakry--{\'E}mery} approach", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "52:1--52:21", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2041", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2041", abstract = "We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry--Emery approach to this setting. In particular, we obtain volume-independent lower bounds for the Glauber dynamics of interacting point particles and for various classes of hardcore models.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Entropy decay, functional inequalities", } @Article{Arguin:2013:ETF, author = "Louis-Pierre Arguin and Anton Bovier and Nicola Kistler", title = "An ergodic theorem for the frontier of branching {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "53:1--53:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2082", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2082", abstract = "We prove a conjecture of Lalley and Sellke [Ann. Probab. 15 (1987)] asserting that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a double exponential, or Gumbel, distribtion with a random shift. The method of proof is based on the decorrelation of the maximal displacements for appropriate time scales. A crucial input is the localization of the paths of particles close to the maximum that was previously established by the authors [Comm. Pure Appl. Math. 64 (2011)].", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching Brownian motion, ergodicity, extreme value theory, KPP equation and traveling waves", } @Article{Barbour:2013:AEC, author = "Andrew Barbour and Gesine Reinert", title = "Approximating the epidemic curve", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "54:1--54:30", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2557", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2557", abstract = "Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that are susceptible follows a more or less deterministic course. In this paper, we show that both of these features are consequences of assuming a locally branching structure in the models, and that the deterministic course can itself be determined from the distribution of the limiting random variable associated with the backward, susceptibility branching process. Examples considered includea stochastic version of the Kermack \& McKendrick model, the Reed--Frost model, and the Volz configuration model.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Epidemics, Reed--Frost, configuration model, deterministic approximation, branching processes", } @Article{Zhang:2013:DIS, author = "Xicheng Zhang", title = "Degenerate irregular {SDEs} with jumps and application to integro-differential equations of {Fokker--Planck} type", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "55:1--55:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2820", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2820", abstract = "We investigate stochastic differential equations with jumps and irregular coefficients, and obtain the existence and uniqueness of generalized stochastic flows. Moreover, we also prove the existence and uniqueness of $ L^p$-solutions or measure-valued solutions for second order integro-differential equation of Fokker--Planck type.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "DiPerna--Lions theory, Generalized stochastic flows, Poisson point processes, Fokker--Planck equations", } @Article{Bouleau:2013:CEL, author = "Nicolas Bouleau and Laurent Denis", title = "Chaotic extensions and the lent particle method for {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "56:1--56:16", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1838", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1838", abstract = "In previous works, we have developed a new Malliavin calculus on the Poisson space based on the {\em lent particle formula}. The aim of this work is to prove that, on the Wiener space for the standard Ornstein--Uhlenbeck structure, we also have such a formula which permits to calculate easily and intuitively the Malliavin derivative of a functional. Our approach uses chaos extensions associated to stationary processes of rotations of normal martingales.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Malliavin calculus, chaotic extensions, normal martingales", } @Article{Brzezniak:2013:ULS, author = "Zdzis{\l}aw Brze{\'z}niak and Erika Hausenblas and El{\.z}bieta Motyl", title = "Uniqueness in Law of the stochastic convolution process driven by {L{\'e}vy} noise", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "57:1--57:15", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2807", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2807", abstract = "We will give a proof of the following fact. If $ \mathfrak {A}_1 $ and $ \mathfrak {A}_2 $, $ \tilde \eta_1 $ and $ \tilde \eta_2 $, $ \xi_1 $ and $ \xi_2 $ are two examples of filtered probability spaces, time homogeneous compensated Poisson random measures, and progressively measurable Banach space valued processes such that the laws on $ L^p([0, T], {L}^p(Z, \nu; E)) \times \mathcal {M}_I([0, T] \times Z) $ of the pairs $ (\xi_1, \eta_1) $ and $ (\xi_2, \eta_2) $, are equal, and $ u_1 $ and $ u_2 $ are the corresponding stochastic convolution processes, then the laws on $ (\mathbb {D}([0, T]; X) \cap L^p([0, T]; B)) \times L^p([0, T], {L}^p(Z, \nu; E)) \times \mathcal {M}_I([0, T] \times Z) $, where $ B \subset E \subset X $, of the triples $ (u_i, \xi_i, \eta_i) $, $ i = 1, 2 $, are equal as well. By $ \mathbb {D}([0, T]; X) $ we denote the Skorokhod space of $X$-valued processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Poisson random measure, stochastic convolution process, uniqueness in law, stochastic partial differential equations", } @Article{Bouchet:2013:SBR, author = "{\'E}lodie Bouchet", title = "Sub-ballistic random walk in {Dirichlet} environment", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "58:1--58:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2109", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2109", abstract = "We consider random walks in Dirichlet environment (RWDE) on $ \mathbb {Z}^d $, for $ d \geq 3 $, in the sub-ballistic case. We associate to any parameter $ (\alpha_1, \dots, \alpha_{2d}) $ of the Dirichlet law a time-change to accelerate the walk. We prove that the continuous-time accelerated walk has an absolutely continuous invariant probability measure for the environment viewed from the particle. This allows to characterize directional transience for the initial RWDE. It solves as a corollary the problem of Kalikow's $ 0 - 1 $ law in the Dirichlet case in any dimension. Furthermore, we find the polynomial order of the magnitude of the original walk's displacement.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dirichlet distribution; Invariant measure viewed from the particle; Random walk in random environment; Reinforced random walks", } @Article{Erdos:2013:LSL, author = "L{\'a}szl{\'o} Erd{\H{o}}s and Antti Knowles and Horng-Tzer Yau and Jun Yin", title = "The local semicircle law for a general class of random matrices", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "59:1--59:58", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2473", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2473", abstract = "We consider a general class of $ N \times N $ random matrices whose entries $ h_{ij} $ are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, $ \max_{i, j} \mathbb {E} \left |h_{ij} \right |^2 $. As a consequence, we prove the universality of the local $n$-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width $ W \gg N^{1 - \varepsilon_n}$ with some $ \varepsilon_n > 0$ and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "eigenvalue rigidity; local semicircle law; Random band matrix; universality", } @Article{Caravenna:2013:IPR, author = "Francesco Caravenna and Lo{\"\i}c Chaumont", title = "An invariance principle for random walk bridges conditioned to stay positive", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "60:1--60:32", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2362", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2362", abstract = "We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the absolutely continuous setting. This includes as a special case the convergence under diffusive rescaling of random walk excursions toward the normalized Brownian excursion, for zero mean, finite variance random walks. The proof exploits a suitable absolute continuity relation together with some local asymptotic estimates for random walks conditioned to stay positive, recently obtained by Vatutin and Wachtel and by Doney. We review and extend these relations to the absolutely continuous setting.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random Walk, Bridge, Excursion, Stable Law, L{\'e}vy Process, Conditioning to Stay Positive, Local Limit Theorem, Invariance Principle", } @Article{Crane:2013:CRM, author = "Harry Crane and Steven Lalley", title = "Convergence rates of {Markov} chains on spaces of partitions", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "61:1--61:23", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2389", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2389", abstract = "We study the convergence rate to stationarity for a class of exchangeable partition-valued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain are determined by products of i.i.d. stochastic matrices, which describe the chain induced on the simplex by taking asymptotic frequencies. Using this representation, we establish upper bounds for the mixing times of ergodic cut-and-paste chains, and under certain conditions on the distribution of the governing random matrices we show that the ``cutoff phenomenon'' holds.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "cut-and-paste chain; cutoff phenomenon; exchangeability; Lyapunov exponent; mixing time", } @Article{Allez:2013:DMM, author = "Romain Allez and Alice Guionnet", title = "A diffusive matrix model for invariant $ \beta $-ensembles", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "62:1--62:30", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2073", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2073", abstract = "We define a new diffusive matrix model converging towards the $ \beta $-Dyson Brownian motion for all $ \beta \in [0, 2]$ that provides an explicit construction of $ \beta $-ensembles of random matrices that is invariant under the orthogonal/unitary group. We also describe the eigenvector dynamics of the limiting matrix process; we show that when $ \beta < 1$ and that two eigenvalues collide, the eigenvectors of these two colliding eigenvalues fluctuate very fast and take the uniform measure on the orthocomplement of the eigenvectors of the remaining eigenvalues.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Dyson Brownian motion; Interacting particles system; random matrices; stochastic calculus", } @Article{Konig:2013:MAB, author = "Wolfgang K{\"o}nig and Onur G{\"u}n and Ozren Sekulovi{\'c}", title = "Moment asymptotics for branching random walks in random environment", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "63:1--63:18", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2212", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2212", abstract = "We consider the long-time behaviour of a branching random walk in random environment on the lattice $ \mathbb {Z}^d $. The migration of particles proceeds according to simple random walk in continuous time, while the medium is given as a random potential of spatially dependent killing/branching rates. The main objects of our interest are the annealed moments $ \langle m_n^p \rangle $, i.e., the $p$-th moments over the medium of the $n$-th moment over the migration and killing/branching, of the local and global population sizes. For $ n = 1$, this is well-understood, as $ m_1$ is closely connected with the parabolic Anderson model. For some special distributions, this was extended to $ n \geq 2$, but only as to the first term of the asymptotics, using (a recursive version of) a Feynman--Kac formula for $ m_n$.\par In this work we derive also the second term of the asymptotics, for a much larger class of distributions. In particular, we show that $ \langle m_n^p \rangle $ and $ \langle m_1^{np} \rangle $ are asymptotically equal, up to an error $ e^{o(t)}$. The cornerstone of our method is a direct Feynman--Kac type formula for $ m_n$, which we establish using known spine techniques.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching random walk, random potential, parabolic Anderson model, Feynman--Kac-type formula, annealed moments, large deviations", } @Article{Sanz-Sole:2013:SWE, author = "Marta Sanz-Sol{\'e} and Andr{\'e} S{\"u}ss", title = "The stochastic wave equation in high dimensions: Malliavin differentiability and absolute continuity", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "64:1--64:28", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2341", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2341", abstract = "We consider the class of non-linear stochastic partial differential equations studied in [Conus-Dalang, 2008]. Equivalent formulations using integration with respect to a cylindrical Brownian motion and also the Skorohod integral are established. It is proved that the random field solution to these equations at any fixed point $ (t, x) \in [0, T] \times \mathbb {R}^d $ is differentiable in the Malliavin sense. For this, an extension of the integration theory in [Conus-Dalang, 2008] to Hilbert space valued integrands is developed, and commutation formulae of the Malliavin derivative and stochastic and pathwise integrals are proved. In the particular case of equations with additive noise, we establish the existence of density for the law of the solution at $ (t, x) \in]0, T] \times \mathbb {R}^d $. The results apply to the stochastic wave equation in spatial dimension $ d \ge 4 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "densities.; Malliavin calculus; stochastic integration; stochastic partial differential equations; stochastic wave equation", } @Article{Joulin:2013:MCT, author = "Ald{\'e}ric Joulin and Arnaud Guillin", title = "Measure concentration through non-{Lipschitz} observables and functional inequalities", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "65:1--65:26", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2425", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2425", abstract = "Non-Gaussian concentration estimates are obtained for invariant probability measures of reversible Markov processes. We show that the functional inequalities approach combined with a suitable Lyapunov condition allows us to circumvent the classical Lipschitz assumption of the observables. Our method is general and offers an unified treatment of diffusions and pure-jump Markov processes on unbounded spaces.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Concentration; diffusion process; functional inequality; invariant measure; jump process; Lyapunov condition; reversible Markov process", } @Article{Grosskinsky:2013:DCS, author = "Stefan Grosskinsky and Frank Redig and Kiamars Vafayi", title = "Dynamics of condensation in the symmetric inclusion process", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "66:1--66:23", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2720", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2720", abstract = "The inclusion process is a stochastic lattice gas, which is a natural bosonic counterpart of the well-studied exclusion process and has strong connections to models of heat conduction and applications in population genetics. Like the zero-range process, due to attractive interaction between the particles, the inclusion process can exhibit a condensation transition. In this paper we present first rigorous results on the dynamics of the condensate formation for this class of models. We study the symmetric inclusion process on a finite set $S$ with total number of particles $N$ in the regime of strong interaction, i.e., with independent diffusion rate $ m = m_N \to 0$. For the case $ N m_N \to \infty $ we show that on the time scale $ 1 / m_N$ condensates emerge from general homogeneous initial conditions, and we precisely characterize their limiting dynamics. In the simplest case of two sites or a fully connected underlying random walk kernel, there is a single condensate hopping over $S$ as a continuous-time random walk. In the non fully connected case several condensates can coexist and exchange mass via intermediate sites in an interesting coarsening process, which consists of a mixture of a diffusive motion and a jump process, until a single condensate is formed. Our result is based on a general two-scale form of the generator, with a fast-scale neutral Wright--Fisher diffusion and a slow-scale deterministic motion. The motion of the condensates is described in terms of the generator of the deterministic motion and the harmonic projection corresponding to the absorbing states of the Wright Fisher diffusion.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coarsening dynamics; condensation; inclusion process; Wright--Fisher diffusion", } @Article{Fathi:2013:TEI, author = "Max Fathi and Noufel Frikha", title = "Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "67:1--67:36", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2586", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2586", abstract = "We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a diffusion process at a fixed deterministic date and the second one concerns the law of a stochastic approximation algorithm at a given time-step. Our results notably improve and complete those obtained in [Frikha, Menozzi, 2012]. The key point is to properly quantify the contribution of the diffusion term to the concentration regime. We also derive a general non-asymptotic deviation bound for the difference between a function of the trajectory of a continuous Euler scheme associated to a diffusion process and its mean. Finally, we obtain non-asymptotic bound for stochastic approximation with averaging of trajectories, in particular we prove that averaging a stochastic approximation algorithm with a slow decreasing step sequence gives rise to optimal concentration rate.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "deviation bounds; Euler scheme; stochastic approximation algorithms; stochastic approximation with averaging; transportation-entropy inequalities", } @Article{Azais:2013:CCR, author = "Jean-Marc Aza{\"\i}s and Jos{\'e} Le{\'o}n", title = "{CLT} for crossings of random trigonometric polynomials", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "68:1--68:17", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2403", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2403", abstract = "We establish a central limit theorem for the number of roots of the equation $ X_N(t) = u $ when $ X_N(t) $ is a Gaussian trigonometric polynomial of degree $N$. The case $ u = 0$ was studied by Granville and Wigman. We show that for some size of the considered interval, the asymptotic behavior is different depending on whether $u$ vanishes or not. Our mains tools are: (a) a chaining argument with the stationary Gaussain process with covariance $ \sin (t) / t$, (b) the use of Wiener chaos decomposition that explains some singularities that appear in the limit when $ u \neq 0$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Chaos expansion; Crossings of random trigonometric polynomials; Rice formula", } @Article{Kozachenko:2013:CGW, author = "Yuriy Kozachenko and Andriy Olenko and Olga Polosmak", title = "On convergence of general wavelet decompositions of nonstationary stochastic processes", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "69:1--69:21", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2234", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2234", abstract = "The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed technique are shown for several classes of stochastic processes. In particular, the main theorem is adjusted to the fractional Brownian motion case. New results on the rate of convergence of the wavelet expansions in the space $ C([0, T]) $ are also presented.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Convergence in probability; Convergence rate; Fractional Brownian motion; Gaussian process; Uniform convergence; Wavelets", } @Article{Assing:2013:SDS, author = "Sigurd Assing and James Bichard", title = "On the spatial dynamics of the solution to the stochastic heat equation", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "70:1--70:32", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2797", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2797", abstract = "We consider the solution of $ \partial_t u = \partial_x^2 u + \partial_x \partial_t B, \, (x, t) \in \mathbb {R} \times (0, \infty) $, subject to $ u(x, 0) = 0, \, x \in \mathbb {R} $, where $B$ is a Brownian sheet. We show that $u$ also satisfies $ \partial_x^2 u + [\, (\partial_t^2)^{1 / 2} + \sqrt {2} \partial_x(\partial_t^2)^{1 / 4} \,] \, u^a = \partial_x \partial_t{\tilde B}$ in $ \mathbb {R} \times (0, \infty)$ where $ u^a$ stands for the extension of $ u(x, t)$ to $ (x, t) \in \mathbb {R}^2$ which is antisymmetric in $t$ and $ \tilde {B}$ is another Brownian sheet. The new SPDE allows us to prove the strong Markov property of the pair $ (u, \partial_x u)$ when seen as a process indexed by $ x \ge x_0$, $ x_0$ fixed, taking values in a state space of functions in $t$. The method of proof is based on enlargement of filtration and we discuss how our method could be applied to other quasi-linear SPDEs.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic partial differential equation, enlargement of filtration, Brownian sheet, Gaussian analysis", } @Article{Komjathy:2013:MRT, author = "J{\'u}lia Komj{\'a}thy and Yuval Peres", title = "Mixing and relaxation time for random walk on wreath product graphs", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "71:1--71:23", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2321", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2321", abstract = "Suppose that $G$ and $H$ are finite, connected graphs, $G$ regular, $X$ is a lazy random walk on $G$ and $Z$ is a reversible ergodic Markov chain on $H$. The generalized lamplighter chain $ X*$ associated with $X$ and $Z$ is the random walk on the wreath product $ H \wr G$, the graph whose vertices consist of pairs $ (f, x)$ where $ f = (f_v)_{v \in V(G)}$ is a labeling of the vertices of $G$ by elements of $H$ and $x$ is a vertex in $G$. In each step, $ X*$ moves from a configuration $ (f, x)$ by updating $x$ to $y$ using the transition rule of $X$ and then independently updating both $ f_x$ and $ f_y$ according to the transition probabilities on $H$; $ f_z$ for $z$ different of $x$, $y$ remains unchanged. We estimate the mixing time of $ X*$ in terms of the parameters of $H$ and $G$. Further, we show that the relaxation time of $ X*$ is the same order as the maximal expected hitting time of $G$ plus $ |G|$ times the relaxation time of the chain on $H$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random Walk, Wreath Product Graphs, Mixing Time, Relaxation Time", } @Article{Blaszczyszyn:2013:CPP, author = "Bartlomiej Blaszczyszyn and Dhandapani Yogeshwaran", title = "Clustering and percolation of point processes", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "72:1--72:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2468", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2468", abstract = "We are interested in phase transitions in certain percolation models on point processes and their dependence on clustering properties of the point processes. We show that point processes with smaller void probabilities and factorial moment measures than the stationary Poisson point process exhibit non-trivial phase transition in the percolation of some coverage models based on level-sets of additive functionals of the point process. Examples of such point processes are determinantal point processes, some perturbed lattices and more generally, negatively associated point processes. Examples of such coverage models are k-coverage in the Boolean model (coverage by at least k grains), and SINR-coverage (coverage if the signal to-interference-and-noise ratio is large). In particular, we answer in affirmative the hypothesis of existence of phase transition in the percolation of k-faces in the Cech simplicial complex (called also clique percolation) on point processes which cluster less than the Poisson process.\par We also construct a Cox point process, which is ``more clustered'' than the Poisson point process and whose Boolean model percolates for arbitrarily small radius. This shows that clustering (at least, as detected by our specific tools) does not always `worsen' percolation, as well as that upper-bounding this clustering by a Poisson process is a consequential assumption for the phase transition to hold.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "point process, Boolean model, percolation, phase transition, shot-noise fields, level-sets, directionally convex ordering, perturbed lattices, determinantal, sub-Poisson point processes", } @Article{Osekowski:2013:SIM, author = "Adam Os{\k{e}}kowski", title = "Sharp inequalities for martingales with values in {$ \ell_\infty^N $}", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "73:1--73:19", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2667", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2667", abstract = "The objective of the paper is to study sharp inequalities for transforms of martingales taking values in $ \ell_\infty^N $. Using Burkholder's method combined with an intrinsic duality argument, we identify, for each $ N \geq 2 $, the best constant $ C_N $ such that the following holds. If $f$ is a martingale with values in $ \ell_\infty^N$ and $g$ is its transform by a sequence of signs, then\par $$ ||g||_1 \leq C_N ||f||_\infty $$. This is closely related to the characterization of UMD spaces in terms of the so-called $ \eta $ convexity, studied in the eighties by Burkholder and Lee.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "best constants; Martingale; transform; UMD space", } @Article{Holroyd:2013:IDT, author = "Alexander Holroyd and Terry Soo", title = "Insertion and deletion tolerance of point processes", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "74:1--74:24", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2621", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2621", abstract = "We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the original process. This condition and the related notion of deletion-tolerance are extensions of the so-called finite energy condition for discrete random processes. We prove several equivalent formulations of each condition, including versions involving Palm processes. Certain other seemingly natural variants of the conditions turn out not to be equivalent. We illustrate the concepts in the context of a number of examples, including Gaussian zero processes and randomly perturbed lattices, and we provide applications to continuum percolation and stable matching.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "point process, finite energy condition, stable matching, continuum percolation", } @Article{Borodin:2013:MDT, author = "Alexei Borodin and Grigori Olshanski", title = "{Markov} dynamics on the {Thoma} cone: a model of time-dependent determinantal processes with infinitely many particles", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "75:1--75:43", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2729", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2729", abstract = "The Thoma cone is an infinite-dimensional locally compact space, which is closely related to the space of extremal characters of the infinite symmetric group $ S_\infty $. In another context, the Thoma cone appears as the set of parameters for totally positive, upper triangular Toeplitz matrices of infinite size.\par The purpose of the paper is to construct a family $ \{ X^{(z, z')} \} $ of continuous time Markov processes on the Thoma cone, depending on two continuous parameters $z$ and $ z'$. Our construction largely exploits specific properties of the Thoma cone related to its representation-theoretic origin, although we do not use representations directly. On the other hand, we were inspired by analogies with random matrix theory coming from models of Markov dynamics related to orthogonal polynomial ensembles.\par We show that processes $ X^{(z, z')}$ possess a number of nice properties, namely: (1) every $ X^{(z, z')}$ is a Feller process; (2) the infinitesimal generator of $ X^{(z, z')}$, its spectrum, and the eigenfunctions admit an explicit description; (3) in the equilibrium regime, the finite-dimensional distributions of $ X^{(z, z')}$ can be interpreted as (the laws of) infinite-particle systems with determinantal correlations; (4) the corresponding time-dependent correlation kernel admits an explicit expression, and its structure is similar to that of time-dependent correlation kernels appearing in random matrix theory.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "determinantal processes; Feller processes; Laguerre polynomials; Markov intertwiners; Meixner polynomials; Thoma cone; Thoma simplex", } @Article{Feray:2013:ABS, author = "Valentin F{\'e}ray", title = "Asymptotic behavior of some statistics in {Ewens} random permutations", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "76:1--76:32", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2496", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2496", abstract = "The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model of random permutations considered here is Ewens sampling model, which generalizes uniform random permutations. Under this model, we describe the asymptotic behavior of some statistics, including the number of occurrences of any dashed pattern. Our approach is based on the method of moments and relies on the following intuition: two events involving the images of different integers are almost independent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random permutations, cumulants, dashed patterns", } @Article{Rippl:2013:NRP, author = "Thomas Rippl and Anja Sturm", title = "New results on pathwise uniqueness for the heat equation with colored noise", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "77:1--77:46", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2506", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2506", abstract = "We consider strong uniqueness and thus also existence of strong solutions for the stochastic heat equation with a multiplicative colored noise term. Here, the noise is white in time and colored in $q$ dimensional space ($ q \geq 1$) with a singular correlation kernel. The noise coefficient is H{\"o}lder continuous in the solution. We discuss improvements of the sufficient conditions obtained in Mytnik, Perkins and Sturm (2006) that relate the H{\"o}lder coefficient with the singularity of the correlation kernel of the noise. For this we use new ideas of Mytnik and Perkins (2011) who treat the case of strong uniqueness for the stochastic heat equation with multiplicative white noise in one dimension. Our main result on pathwise uniqueness confirms a conjecture that was put forward in their paper.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Heat equation, colored noise, stochastic partial differential equation, pathwise uniqueness, existence", } @Article{Carrapatoso:2013:CEC, author = "Kleber Carrapatoso and Amit Einav", title = "Chaos and entropic chaos in {Kac}'s model without high moments", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "78:1--78:38", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2683", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2683", abstract = "In this paper we present a new local L{\'e}vy Central Limit Theorem, showing convergence to stable states that are not necessarily the Gaussian, and use it to find new and intuitive entropically chaotic families with underlying one-particle function that has moments of order $ 2 \alpha $, with $ 1 < \alpha < 2 $. We also discuss a lower semi continuity result for the relative entropy with respect to our specific family of functions, and use it to show a form of stability property for entropic chaos in our settings.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Entropic Chaos; Entropic Stability; Entropy; Kac's model; Local L{\'e}vy central theorem", } @Article{Zhao:2013:MLA, author = "Minzhi Zhao and Huizeng Zhang", title = "On the maximal length of arithmetic progressions", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "79:1--79:21", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2018", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2018", abstract = "This paper is a continuation of a paper by Benjamini, Yadin and Zeitouni's on maximal arithmetic progressions in random subsets. In this paper the asymptotic distributions of the maximal arithmetic progressions and arithmetic progressions modulo $n$ relative to an independent Bernoulli sequence with parameter $p$ are given. The errors are estimated by using the Chen-Stein method. Then the almost sure limit behaviour of these statistics is discussed. Our work extends the previous results and gives an affirmative answer to the conjecture raised at the end of that paper.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "arithmetic progression; Bernoulli sequence; Chen-Stein method; limit distribution", } @Article{Birkner:2013:DRW, author = "Matthias Birkner and Jiri Cerny and Andrej Depperschmidt and Nina Gantert", title = "Directed random walk on the backbone of an oriented percolation cluster", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "80:1--80:35", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2302", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2302", abstract = "We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the ``ancestral lineage'' of an individual in the stationary discrete-time contact process. We prove a law of large numbers and an annealed central limit theorem (i.e., averaged over the realisations of the cluster) using a regeneration approach. Furthermore, we obtain a quenched central limit theorem (i.e., for almost any realisation of the cluster) via an analysis of joint renewals of two independent walks on the same cluster.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walk, dynamical random environment, oriented percolation, supercritical cluster, central limit theorem in random environment", } @Article{Gadat:2013:LDP, author = "S{\'e}bastien Gadat and Fabien Panloup and Cl{\'e}ment Pellegrini", title = "Large deviation principle for invariant distributions of memory gradient diffusions", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "81:1--81:34", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2031", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2031", abstract = "In this paper, we consider a class of diffusion processes based on a memory gradient descent, i.e. whose drift term is built as the average all along the trajectory of the gradient of a coercive function U. Under some classical assumptions on U, this type of diffusion is ergodic and admits a unique invariant distribution. In view to optimization applications, we want to understand the behaviour of the invariant distribution when the diffusion coefficient goes to 0. In the non-memory case, the invariant distribution is explicit and the so-called Laplace method shows that a Large Deviation Principle (LDP) holds with an explicit rate function, that leads to a concentration of the invariant distribution around the global minimums of U. Here, excepted in the linear case, we have no closed formula for the invariant distribution but we show that a LDP can be obtained. Then, in the one-dimensional case, we get some bounds for the rate function that lead to the concentration around the global minimum under some assumptions on the second derivative of U.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Freidlin and Wentzell Theory; Hamilton--Jacobi Equations; hypoelliptic diffusions.; Large Deviation Principle; small stochastic perturbations", } @Article{Cioica:2013:RBS, author = "Petru Cioica and Kyeong-Hun Kim and Kijung Lee and Felix Lindner", title = "On the {$ L_q(L_p) $}-regularity and {Besov} smoothness of stochastic parabolic equations on bounded {Lipschitz} domains", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "82:1--82:41", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2478", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2478", abstract = "We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $ \mathcal {O} \subset \mathbb {R}^d $ with both theoretical and numerical purpose. We use N. V. Krylov's framework of stochastic parabolic weighted Sobole spaces $ \mathfrak {H}^{\gamma, q}_{p, \theta }(\mathcal {O}, T) $. The summability parameters $p$ and $q$ in space and time may differ. Existence and uniqueness of solutions in these spaces is established and the H{\"o}lder regularity in time is analysed. Moreover, we prove a general embedding of weighte $ L_p(\mathcal {O})$-Sobolev spaces into the scale o Besov spaces $ B^\alpha_{\tau, \tau }(\mathcal {O})$, $ 1 / \tau = \alpha / d + 1 / p$, $ \alpha > 0$. This leads to a H{\"o}lder-Besov regularity result for the solution process. The regularity in this Besov scale determines the order of convergence that can be achieved by certain nonlinear approximation schemes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "$L_q(L_p)$-theory; adaptive numerical method; Besov space; embedding theorem; Lipschitz domain; nonlinear approximation; H{\"o}lder regularity in time; quasi-Banach space; Stochastic partial differential equation; wavelet; weighted Sobolev space", } @Article{Falgas-Ravry:2013:DCN, author = "Victor Falgas-Ravry", title = "Distribution of components in the $k$-nearest neighbour random geometric graph for $k$ below the connectivity threshold", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "83:1--83:22", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2465", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2465", abstract = "Let $ S_{n, k} $ denote the random geometric graph obtained by placing points inside a square of area $n$ according to a Poisson point process of intensity $1$ and joining each such point to the $ k = k(n)$ points of the process nearest to it.\par In this paper we show that if $ \mathbb {P}(S_{n, k} \textrm { connected}) > n^{- \gamma_1}$ then the probability that $ S_{n, k}$ contains a pair of `small' components `close' to each other is $ o(n^{-c_1})$ (in a precise sense of `small' and 'close'), for some absolute constants $ \gamma_1 > 0$ and $ c_1 > 0$. This answers a question of Walters. (A similar result was independently obtained by Balister.)\par As an application of our result, we show that the distribution of the connected components of $ S_{n, k}$ below the connectivity threshold is asymptotically Poisson.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random geometric graphs", } @Article{Depperschmidt:2013:PPT, author = "Andrej Depperschmidt and Andreas Greven and Peter Pfaffelhuber", title = "Path-properties of the tree-valued {Fleming--Viot} process", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "84:1--84:47", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2514", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2514", abstract = "We consider the tree-valued Fleming--Viot process, $ (X t) $, $ t \geq 0 $, with mutation and selection. This process models the stochastic evolution of the genealogies and (allelic) types under resampling, mutation and selection in the population currently alive in the limit of infinitely large populations. Genealogies and types are described by (isometry classes of) marked metric measure spaces. The long-time limit of the neutral tree-valued Fleming--Viot dynamics is an equilibrium given via the marked metric measure space associated with the Kingman coalescent.\par In the present paper we pursue two closely linked goals. First, we show that two well-known properties of the Fleming--Viot genealogies at fixed time t arising from the properties of the dual, namely the Kingman coalescent, hold for the whole path. These properties are related to the geometry of the family tree close to its leaves. In particular we consider the number and the size of subfamilies whose individuals are not further than ? apart in the limit ? ? 0. Second, we answer two open questions about the sample paths of the tree-valued Fleming--Viot process. We show that for all t > 0 almost surely the marked metric measure space Xt has no atoms and admits a mark function. The latter property means that all individuals in the tree-valued Fleming--Viot process can uniquely be assigned a type. All main results are proven for the neutral case and then carried over to selective cases via Girsanov's formula giving absolute continuity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Marked tree-valued Fleming--Viot process, path properties, selection, mutation, Kingman coalescent", } @Article{Yao:2013:CWA, author = "Changlong Yao", title = "A {CLT} for winding angles of the arms for critical planar percolation", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "85:1--85:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2285", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2285", abstract = "Consider critical percolation in two dimensions. Under the condition that there are k disjoint alternating open and closed arms crossing the annulus $ A(l, n) $, we prove a central limit theorem and variance estimates for the winding angles of the arms (as $ n \rightarrow \infty $, $l$ fixed). This result confirms a prediction of Beffara and Nolin (Ann. Probab. 39: 1286-1304, 2011). Using this theorem, we also get a CLT for the multiple-armed incipient infinite cluster (IIC) measures.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "arm events.; central limit theorem; critical percolation; incipient infinite cluster; martingale; winding angle", } @Article{Cipriani:2013:HPM, author = "Alessandra Cipriani", title = "High points for the membrane model in the critical dimension", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "86:1--86:17", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2750", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2750", abstract = "In this notice we study the fractal structure of the set of high points for the membrane model in the critical dimension $ d = 4 $. We are able to compute the Hausdorff dimension of the set of points which are atypically high, and also that of clusters, showing that high points tend not to be evenly spread on the lattice. We will see that these results follow closely those obtained by O. Daviaud for the 2-dimensional discrete Gaussian Free Field.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "biLaplacian; extrema of Gaussian fields; Hausdorff dimension; Membrane Model; multiscale decomposition", } @Article{Berger:2013:DTR, author = "Noam Berger and Yuval Peres", title = "Detecting the trail of a random walker in a random scenery", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "87:1--87:18", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2367", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2367", abstract = "Suppose that the vertices of the lattice $ \mathbb {Z}^d $ are endowed with a random scenery, obtained by tossing a fair coin at each vertex. A random walker, starting from the origin, replaces the coins along its path by i.i.d. biased coins. For which walks and dimensions can the resulting scenery be distinguished from the original scenery? We find the answer for simple random walk, where it does not depend on dimension, and for walks with a nonzero mean, where a transition occurs between dimensions three and four. We also answer this question for other types of graphs and walks, and raise several new questions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walk, Random scenery, Relative entropy, Branching number", } @Article{Kraaij:2013:SPM, author = "Richard Kraaij", title = "Stationary product measures for conservative particle systems and ergodicity criteria", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "88:1--88:33", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2513", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2513", abstract = "We study conservative particle systems on $ W^S $, where $S$ is countable and $ W = \{ 0, \dots, N \} $ or $ W = \mathbb {N}$, where the generator reads\par $$ L f(\eta) = \sum_{x, y} p(x, y) b(\eta_x, \eta_y) (f(\eta - \delta_x + \delta_y) - f(\eta)). $$ \par Under assumptions on $b$ and the assumption that $p$ is finite range, which allow for the exclusion, zero range and misanthrope processes, we determine exactly what the stationary product measures are. \par Furthermore, under the condition that $ p + p^*$, $ p^*(x, y) := p(y, x)$, is irreducible, we show that a stationary measure $ \mu $ is ergodic if and only if the tail sigma algebra of the partial sums is trivial under $ \mu $. This is a consequence of a more general result on interacting particle systems that shows that a stationary measure is ergodic if and only if the sigma algebra of sets invariant under the transformations of the process is trivial. We apply this result combined with a coupling argument to the stationary product measures to determine which product measures are ergodic. For the case that $W$ is finite, this gives a complete characterisation.\par In the case that $ W = \mathbb {N}$, it holds for nearly all functions $b$ that a stationary product measure is ergodic if and only if it is supported by configurations with an infinite amount of particles. We show that this picture is not complete. We give an example of a system where $b$ is such that there is a stationary product measure which is not ergodic, even though it concentrates on configurations with an infinite number of particles.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Exclusion process; misanthrope process, stationary product measures, ergodic measures, coupling; zero-range process", } @Article{Normand:2013:RWV, author = "Raoul Normand and B{\'a}lint Vir{\'a}g", title = "Random walks veering left", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "89:1--89:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2523", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2523", abstract = "We study coupled random walks in the plane such that, at each step, the walks change direction by a uniform random angle plus an extra deterministic angle $ \theta $. We compute the Hausdorff dimension of the $ \theta $ for which the walk has an unusual behavior. This model is related to a study of the spectral measure of some random matrices. The same techniques allow to study the boundary behavior of some Gaussian analytic functions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "coupling; Gaussian analytic function; Hausdorff dimension; random matrix; Random walk", } @Article{Rohan:2013:GEA, author = "Neelabh Rohan and T. V. Ramanathan", title = "Geometric ergodicity of asymmetric volatility models with stochastic parameters", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "90:1--90:12", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-1871", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/1871", abstract = "In this paper, we consider a general family of asymmetric volatility models with stationary and ergodic coefficients. This family can nest several non-linear asymmetric GARCH models with stochastic parameters into its ambit. It also generalizes Markov-switching GARCH and GJR models. The geometric ergodicity of the proposed process is established. Sufficient conditions for stationarity and existence of moments have also been investigated. Geometric ergodicity of various volatility models with stochastic parameters has been discussed as special cases.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Asymmetric volatility models; geometric ergodicity; irreducibility; stationarity, stochastic parameter GARCH model", } @Article{Privault:2013:PAC, author = "Nicolas Privault and Giovanni Luca Torrisi", title = "Probability approximation by {Clark--Ocone} covariance representation", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "91:1--91:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2787", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2787", abstract = "Based on the Stein method and a general integration by parts framework we derive various bounds on the distance between probability measures. We show that this framework can be implemented on the Poisson space by covariance identities obtained from the Clark--Ocone representation formula and derivation operators. Our approach avoids the use of the inverse of the Ornstein Uhlenbeck operator as in the existing literature, and also applies to the Wiener space.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Poisson space, Stein--Chen method, Malliavin calculus, Clark--Ocone formula", } @Article{Merkl:2013:PAV, author = "Franz Merkl and Silke Rolles", title = "Perturbation analysis of the {van den Berg Kesten} inequality for determinantal probability measures", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "92:1--92:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2339", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2339", abstract = "This paper describes a second order perturbation analysis of the BK property in the space of Hermitean determinantal probability measures around the subspace of product measures, showing that the second order Taylor approximation of the BK inequality holds for increasing events.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "BK inequality, determinantal probability measure, negative association, Reimer's inequality", } @Article{Saloff-Coste:2013:LDS, author = "Laurent Saloff-Coste and Tianyi Zheng", title = "Large deviations for stable like random walks on {$ \mathbb Z^d $} with applications to random walks on wreath products", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "93:1--93:35", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2439", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2439", abstract = "We derive Donsker--Vardhan type results for functionals of the occupation times when the underlying random walk on $ \mathbb Z^d $ is in the domain of attraction of an operator stable law on $ \mathbb R^d $. Applications to random walks on wreath products (also known as lamplighter groups) are given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Large deviation; Operator-stable laws; Random walk", } @Article{Chen:2013:ASS, author = "Wei-Kuo Chen", title = "The {Aizenman--Sims--Starr} scheme and {Parisi} formula for mixed $p$-spin spherical models", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "94:1--94:14", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2580", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2580", abstract = "The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd p. We establish the Aizenman Sims-Starr scheme and from this together with many well-known results and Dmitry Panchenko's recent proof on the Parisi ultrametricity conjecture, we prove the Parisi formula.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{OConnell:2013:WVR, author = "Neil O'Connell and Yuchen Pei", title = "A $q$-weighted version of the {Robinson--Schensted} algorithm", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "95:1--95:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2930", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2930", abstract = "We introduce a $q$-weighted version of the Robinson--Schensted (column insertion) algorithm which is closely connected to q Whittaker functions (or Macdonald polynomials with t=0) and reduces to the usual Robinson--Schensted algorithm when q=0. The q-insertion algorithm is `randomised', or `quantum', in the sense that when inserting a positive integer into a tableau, the output is a distribution of weights on a particular set of tableaux which includes the output which would have been obtained via the usual column insertion algorithm. There is also a notion of recording tableau in this setting. We show that the distribution of weights of the pair of tableaux obtained when one applies the q-insertion algorithm to a random word or permutation takes a particularly simple form and is closely related to q-Whittaker functions. In the case $ 0 \leq q < 1 $, the q-insertion algorithm applied to a random word also provides a new framework for solving the q-TASEP interacting particle system introduced (in the language of q-bosons) by Sasamoto and Wadati (1998) and yields formulas which are equivalent to some of those recently obtained by Borodin and Corwin (2011) via a stochastic evolution on discrete Gelfand--Tsetlin patterns (or semistandard tableaux) which is coupled to the q-TASEP. We show that the sequence of P-tableaux obtained when one applies the q-insertion algorithm to a random word defines another, quite different, evolution on semistandard tableaux which is also coupled to the q-TASEP.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Macdonald polynomials; q-Whittaker functions", } @Article{Comets:2013:LDC, author = "Francis Comets and Christophe Gallesco and Serguei Popov and Marina Vachkovskaia", title = "On large deviations for the cover time of two-dimensional torus", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "96:1--96:18", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2856", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2856", abstract = "Let $ \mathcal {T}_n $ be the cover time of two-dimensional discrete torus $ \mathbb {Z}^2_n = \mathbb {Z}^2 / n \mathbb {Z}^2 $. We prove that $ \mathbb {P}[\mathcal {T}_n \leq \frac {4}{\pi } \gamma n^2 \ln^2 n] = \exp ( - n^{2(1 - \sqrt {\gamma }) + o(1)}) $ for $ \gamma \in (0, 1) $. One of the main methods used in the proofs is the decoupling of the walker's trace into independent excursions by means of soft local times.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "hitting time; simple random walk; soft local time", } @Article{Ioffe:2013:ASC, author = "Dmitry Ioffe and Yvan Velenik", title = "An almost sure {CLT} for stretched polymers", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "97:1--97:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2231", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2231", abstract = "We prove an almost sure central limit theorem (CLT) for spatial extension of stretched (meaning subject to a non-zero pulling force) polymers at very weak disorder in all dimensions $ d + 1 \geq 4 $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Polymers, random walk representation, random environment, weak disorder, CLT", } @Article{Jerison:2013:IDH, author = "David Jerison and Lionel Levine and Scott Sheffield", title = "Internal {DLA} in higher dimensions", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "98:1--98:14", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-3137", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3137", abstract = "Let $ A(t) $ denote the cluster produced by internal diffusion limited aggregation (internal DLA) with $t$ particles in dimension $ d \geq 3$. We show that $ A(t)$ is approximately spherical, up to an $ O(\sqrt {\log t})$ error.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "discrete harmonic function; internal diffusion limited aggregation; martingale; mean value property; sublogarithmic fluctuations", } @Article{Eisenbaum:2013:IPP, author = "Nathalie Eisenbaum", title = "Inequalities for permanental processes", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "99:1--99:15", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2919", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2919", abstract = "Permanental processes are a natural extension of the definition of squared Gaussian processes. Each one-dimensional marginal of a permanental process is a squared Gaussian variable, but there is not always a Gaussian structure for the entire process. The interest to better know them is highly motivated by the connection established by Eisenbaum and Kaspi, between the infinitely divisible permanental processes and the local times of Markov processes. Unfortunately the lack of Gaussian structure for general permanental processes makes their behavior hard to handle. We present here an analogue for infinitely divisible permanental vectors, of some well-known inequalities for Gaussian vectors.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Permanental process, Gaussian process, infinite divisibility, Slepian lemma, concentration inequality", } @Article{Dirksen:2013:PSI, author = "Sjoerd Dirksen and Jan Maas and Jan Neerven", title = "{Poisson} stochastic integration in {Banach} spaces", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "100:1--100:28", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2945", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2945", abstract = "We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non-trivial martingale (co)type and extend various results in the literature. We also develop a Malliavin framework to interpret Poisson stochastic integrals as vector-valued Skorohod integrals, and prove a Clark--Ocone representation formula.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic integration, Poisson random measure, martingale type, UMD Banach spaces, stochastic convolutions, Malliavin calculus, Clark--Ocone representation theorem", } @Article{Stephenson:2013:GFT, author = "Robin Stephenson", title = "General fragmentation trees", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "101:1--101:45", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2703", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2703", abstract = "We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "continuum random trees; fragmentation trees; self-similar fragmentations", } @Article{Bahlali:2013:PMN, author = "Khaled Bahlali and Lucian Maticiuc and Adrian Zalinescu", title = "Penalization method for a nonlinear {Neumann PDE} via weak solutions of reflected {SDEs}", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "102:1--102:19", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2467", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2467", abstract = "In this paper we prove an approximation result for the viscosity solution of a system of semi-linear partial differential equations with continuous coefficients and nonlinear Neumann boundary condition. The approximation we use is based on a penalization method and our approach is probabilistic. We prove the weak uniqueness of the solution for the reflected stochastic differential equation and we approximate it (in law) by a sequence of solutions of stochastic differential equations with penalized terms. Using then a suitable generalized backward stochastic differential equation and the uniqueness of the reflected stochastic differential equation, we prove the existence of a continuous function, given by a probabilistic representation, which is a viscosity solution of the considered partial differential equation. In addition, this solution is approximated by the penalized partial differential equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Backward stochastic differential equations; Jakubowski S-topology; Penalization method; Reflecting stochastic differential equation; Weak solution", } @Article{Mountford:2013:MDC, author = "Thomas Mountford and Daniel Valesin and Qiang Yao", title = "Metastable densities for the contact process on power law random graphs", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "103:1--103:36", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2512", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2512", abstract = "We consider the contact process on a random graph with fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett (2009), who showed that for arbitrarily small infection parameter $ \lambda $, the survival time of the process is larger than a stretched exponential function of the number of vertices, $n$. We obtain sharp bounds for the typical density of infected sites in the graph, as $ \lambda $ is kept fixed and $n$ tends to infinity. We exhibit three different regimes for this density, depending on the tail of the degree law.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "contact process, random graphs", } @Article{Kunze:2013:CMP, author = "Markus Kunze", title = "On a class of martingale problems on {Banach} spaces", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "104:1--104:30", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2924", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2924", abstract = "We introduce the local martingale problem associated to semilinear stochastic evolution equations driven by a cylindrical Wiener process and establish a one-to-one correspondence between solutions of the martingale problem and (analytically) weak solutions of the stochastic equation. We also prove that the solutions of well-posed equations are strong Markov processes. We apply our results to semilinear stochastic equations with additive noise where the semilinear term is merely measurable and to stochastic reaction-diffusion equations with H{\"o}lder continuous multiplicative noise.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "local Martingale problem, strong Markov property, stochastic partial differential equations", } @Article{Damron:2013:FCD, author = "Michael Damron and Hana Kogan and Charles Newman and Vladas Sidoravicius", title = "Fixation for coarsening dynamics in {$2$D} slabs", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "105:1--105:20", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-3059", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3059", abstract = "We study zero-temperature Ising Glauber Dynamics, on $ 2 D $ slabs of thickness $ k \geq 2 $. In this model, $ \pm 1$-valued spins at integer sites update according to majority vote dynamics with two opinions. We show that all spins reaches a final state (that is, the system fixates) for $ k = 2$ under free boundary conditions and for $ k = 2$ or $3$ under periodic boundary conditions. For thicker slabs there are sites that fixate and sites that do not.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Coarsening, Glauber Dynamics, Ising model", } @Article{Bansaye:2013:ECS, author = "Vincent Bansaye and Juan Carlos Pardo Millan and Charline Smadi", title = "On the extinction of continuous state branching processes with catastrophes", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "106:1--106:31", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2774", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2774", abstract = "We consider continuous state branching processes (CSBP's) with additional multiplicative jumps modeling dramatic events in a random environment. These jumps are described by a L{\'e}vy process with bounded variation paths. We construct the associated class of processes as the unique solution of a stochastic differential equation. The quenched branching property of the process allows us to derive quenched and annealed results and make appear new asymptotic behaviors. We characterize the Laplace exponent of the process as the solution of a backward ordinary differential equation and establish when it becomes extinct. For a class of processes for which extinction and absorption coincide (including the $ \alpha $ stable CSBP's plus a drift), we determine the speed of extinction. Four regimes appear, as in the case of branching processes in random environment in discrete time and space. The proofs rely on a fine study of the asymptotic behavior of exponential functionals of L{\'e}vy processes. Finally, we apply these results to a cell infection model and determine the mean speed of propagation of the infection.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Continuous State Branching Processes, L{\'e}vy processes, Poisson Point Processes, Random Environment, Extinction, Long time behavior", } @Article{Youssef:2013:ECR, author = "Pierre Youssef", title = "Estimating the covariance of random matrices", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "107:1--107:26", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2579", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2579", abstract = "We extend to the matrix setting a recent result of Srivastava--Vershynin about estimating the covariance matrix of a random vector. The result can be interpreted as a quantified version of the law of large numbers for positive semi-definite matrices which verify some regularity assumption. Beside giving examples, we discuss the notion of log-concave matrices and give estimates on the smallest and largest eigenvalues of a sum of such matrices.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Riedel:2013:SPD, author = "Sebastian Riedel and Weijun Xu", title = "A simple proof of distance bounds for {Gaussian} rough paths", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "108:1--108:18", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2387", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2387", abstract = "We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assumption of their covariance functions. Similar estimates have been obtained recently in [Friz-Riedel, AIHP, to appear]. One advantage of our argument is that we obtain the bound for the third level iterated integrals merely based on the first two levels, and this reflects the intrinsic nature of rough paths. Our estimates are sharp when both covariance functions have finite $1$-variation, which includes a large class of Gaussian processes. Two applications of our estimates are discussed. The first one gives the a.s. convergence rates for approximated solutions to rough differential equations driven by Gaussian processes. In the second example, we show how to recover the optimal time regularity for solutions of some rough SPDEs.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian rough paths, iterated integrals, signatures", } @Article{Pham:2013:SNE, author = "Triet Pham and Jianfeng Zhang", title = "Some norm estimates for semimartingales", journal = j-ELECTRON-J-PROBAB, volume = "18", pages = "109:1--109:25", year = "2013", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v18-2406", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2406", abstract = "In this paper we introduce a new type of norms for semimartingales, under both linear and nonlinear expectations. Our norm is defined in the spirit of quasimartingales, and it characterizes square integrable semimartingales. This work is motivated by our study of zero-sum stochastic differential games, whose value process is conjectured to be a semimartingale under a class of probability measures. As a by product, we establish some a priori estimates for doubly reflected BSDEs without imposing the Mokobodski's condition directly.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Semimartingale, quasimartingale, $G$-expectation, second order backward SDEs, doubly reflected backward SDEs, Doob--Meyer decomposition", } @Article{Gu:2014:IPB, author = "Yu Gu and Guillaume Bal", title = "An invariance principle for {Brownian} motion in random scenery", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "1:1--1:19", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2894", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2894", abstract = "We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension $ d = 2 $, which is the main new contribution of the paper.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "weak convergence, random media, central limit theorem", } @Article{Abraham:2014:LLCa, author = "Romain Abraham and Jean-Fran{\c{c}}ois Delmas", title = "Local limits of conditioned {Galton--Watson} trees: the infinite spine case", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "2:1--2:19", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2747", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2747", abstract = "We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton--Watson tree to Kesten's tree. This yields elementary proofs of Kesten's result as well as other known results on local limit of conditioned Galton--Watson trees. We then apply this condition to get new results, in the critical and sub-critical cases, on the limit in distribution of a Galton--Watson tree conditioned on having a large number of individuals with out-degree in a given set.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Conditioned Galton--Watson tree, Kesten's tree", } @Article{Sulzbach:2014:GLP, author = "Henning Sulzbach and Ralph Neininger and Michael Drmota", title = "A {Gaussian} limit process for optimal {FIND} algorithms", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "3:1--3:28", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2933", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2933", abstract = "We consider versions of the FIND algorithm where the pivot element used is the median of a subset chosen uniformly at random from the data. For the median selection we assume that subsamples of size asymptotic to $ c \cdot n^\alpha $ are chosen, where $ 0 < \alpha \leq \frac {1}{2} $, $ c > 0 $ and $n$ is the size of the data set to be split. We consider the complexity of FIND as a process in the rank to be selected and measured by the number of key comparisons required. After normalization we show weak convergence of the complexity to a centered Gaussian process as $ n \to \infty $, which depends on $ \alpha $. The proof relies on a contraction argument for probability distributions on c{\`a}dl{\`a}g functions. We also identify the covariance function of the Gaussian limit process and discuss path and tail properties.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "FIND algorithm, Quickselect, complexity, key comparisons, functional limit theorem, contraction method, Gaussian process", } @Article{Sheffield:2014:TPR, author = "Scott Sheffield and Ariel Yadin", title = "Tricolor percolation and random paths in {$3$D}", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "4:1--4:23", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3073", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3073", abstract = "We study ``tricolor percolation'' on the regular tessellation of $ \mathbb {R}^3 $ by truncated octahedra, which is the three-dimensional analog of the hexagonal tiling of the plane. We independently assign one of three colors to each cell according to a probability vector $ p = (p_1, p_2, p_3) $ and define a ``tricolor edge'' to be an edge incident to one cell of each color. The tricolor edges form disjoint loops and/or infinite paths. These loops and paths have been studied in the physics literature, but little has been proved mathematically.\par We show that each $p$ belongs to either the {\em compact phase} (in which the length of the tricolor loop passing through a fixed edge is a.s. finite, with exponentially decaying law) or the {\em extended phase} (in which the probability that an $ (n \times n \times n)$ box intersects a tricolor path of diameter at least $n$ exceeds a positive constant, independent of $n$). We show that both phases are non-empty and the extended phase is a closed subset of the probability simplex.\par We also survey the physics literature and discuss open questions, including the following: Does $ p = (1 / 3, 1 / 3, 1 / 3) $ belong to the extended phase? Is there a.s. an infinite tricolor path for this $p$ ? Are there infinitely many? Do they scale to Brownian motion? If $p$ lies on the boundary of the extended phase, do the long paths have a scaling limit analogous to SLE6 in two dimensions? What can be shown for the higher dimensional analogs of this problem?", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "tricolor percolation, vortex models, truncated octahedron, body centered cubic lattice, permutahedron", } @Article{Holroyd:2014:SDC, author = "Alexander Holroyd and James Martin", title = "Stochastic domination and comb percolation", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "5:1--5:16", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2806", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2806", abstract = "There exists a Lipschitz embedding of a d-dimensional comb graph (consisting of infinitely many parallel copies of $ \mathbb {Z}^{d - 1} $ joined by a perpendicular copy) into the open set of site percolation on $ \mathbb {Z}^d $, whenever the parameter $p$ is close enough to 1 or the Lipschitz constant is sufficiently large. This is proved using several new results and techniques involving stochastic domination, in contexts that include a process of independent overlapping intervals on $ \mathbb {Z} $, and first-passage percolation on general graphs.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "stochastic domination, percolation, comb graph, Lipschitz embedding, first-passage percolation", } @Article{Duquesne:2014:EPC, author = "Thomas Duquesne and Cyril Labb{\'e}", title = "On the {Eve} property for {CSBP}", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "6:1--6:31", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2831", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2831", abstract = "We consider the population model associated to continuous state branching processes and we are interested in the so-called Eve property that asserts the existence of an ancestor with an overwhelming progeny at large times, and more generally, in the possible behaviours of the frequencies among the population at large times. In this paper, we classify all the possible behaviours according to the branching mechanism of the continuous state branching process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Continuous state branching process; dust; Eve; frequency distribution; Grey martingale", } @Article{Mijatovic:2014:MCA, author = "Aleksandar Mijatovic and Matija Vidmar and Saul Jacka", title = "{Markov} chain approximations for transition densities of {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "7:1--7:37", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2208", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2208", abstract = "We consider the convergence of a continuous-time Markov chain approximation $ X^h $, $ h > 0 $, to an $ \mathbb {R}^d$-valued L{\'e}vy process $X$. The state space of $ X^h$ is an equidistant lattice and its $Q$-matrix is chosen to approximate the generator of $X$. In dimension one ($ d = 1$), and then under a general sufficient condition for the existence of transition densities of $X$, we establish sharp convergence rates of the normalised probability mass function of $ X^h$ to the probability density function of $X$. In higher dimensions ($ d > 1$), rates of convergence are obtained under a technical condition, which is satisfied when the diffusion matrix is non-degenerate.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Levy process, continuous-time Markov chain, spectral representation, convergence rates for semi-groups and transition densities", } @Article{Graf:2014:FFM, author = "Robert Graf", title = "A forest-fire model on the upper half-plane", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "8:1--8:27", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2625", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2625", abstract = "We consider a discrete forest-fire model on the upper half-plane of the two-dimensional square lattice. Each site can have one of the following two states: ``vacant'' or ``occupied by a tree''. At the starting time all sites are vacant. Then the process is governed by the following random dynamics: Trees grow at rate 1, independently for all sites. If an occupied cluster reaches the boundary of the upper half plane or if it is about to become infinite, the cluster is instantaneously destroyed, i.e., all of its sites turn vacant. Additionally, we demand that the model is invariant under translations along the x-axis. We prove that such a model exists and arises naturally as a subseqential limit of forest-fire processes in finite boxes when the box size tends to infinity. Moreover, the model exhibits a phase transition in the following sense: There exists a critical time $ t_c $ (which corresponds with the critical probability $ p_c $ in ordinary site percolation by $ 1 - e^{-t_c} = p_c$) such that before $ t_c$, only sites close to the boundary have been affected by destruction, whereas after $ t_c$, sites on the entire half-plane have been affected by destruction.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "forest-fire model, upper half-plane, self-organized criticality, phase transition", } @Article{Dedecker:2014:SAE, author = "J{\'e}r{\^o}me Dedecker and Emmanuel Rio and Florence Merlev{\`e}de", title = "Strong approximation of the empirical distribution function for absolutely regular sequences in {$ {\mathbb R}^d $}", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "9:1--9:56", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2658", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2658", abstract = "We prove a strong approximation result with rates for the empirical process associated to an absolutely regular stationary sequence of random variables with values in $ {\mathbb R}^d $. As soon as the absolute regular coefficients of the sequence decrease more rapidly than $ n^{1 - p} $ for some $ p \in]2, 3] $, we show that the error of approximation between the empirical process and a two-parameter Gaussian process is of order $ n^{1 / p} (\log n)^{\lambda (d)} $ for some positive $ \lambda (d) $ depending on $d$, both in $ {\mathbb L}^1$ and almost surely. The power of $n$ being independent of the dimension, our results are even new in the independent setting, and improve earlier results. In addition, for absolutely regular sequences, we show that the rate of approximation is optimal up to the logarithmic term.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Strong approximation, Kiefer process, empirical process, stationary sequences, absolutely regular sequences", } @Article{Lochowski:2014:ILL, author = "Rafa{\l} Marcin {\L}ochowski and Raouf Ghomrasni", title = "Integral and local limit theorems for level crossings of diffusions and the {Skorohod} problem", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "10:1--10:33", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2644", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2644", abstract = "Using a new technique, based on the regularisation of a c{\`a}dl{\`a}g process via the double Skorohod map, we obtain limit theorems for integrated numbers of level crossings of diffusions. This result is related to the recent results on the limit theorems for the truncated variation. We also extend to diffusions the classical result of Kasahara on the ``local'' limit theorem for the number of crossings of a Wiener process. We establish the correspondence between the truncated variation and the double Skorohod map. Additionally, we prove some auxiliary formulas for the Skorohod map with time-dependent boundaries.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "level crossings, interval crossings, the Skorohod problem, diffusions; local time; semimartingales; truncated variation", } @Article{Applebaum:2014:SQS, author = "David Applebaum and Jan Neerven", title = "Second quantisation for skew convolution products of measures in {Banach} spaces", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "11:1--11:17", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3031", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3031", abstract = "We study measures in Banach space which arise as the skew convolution product of two other measures where the convolution is deformed by a skew map. This is the structure that underlies both the theory of Mehler semigroups and operator self-decomposable measures. We show how that given such a set-up the skew map can be lifted to an operator that acts at the level of function spaces and demonstrate that this is an example of the well known functorial procedure of second quantisation. We give particular emphasis to the case where the product measure is infinitely divisible and study the second quantisation process in some detail using chaos expansions when this is either Gaussian or is generated by a Poisson random measure.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Second quantisation, skew convolution family, infinitely divisible measure, Wiener--It{\^o} decomposition, Poisson random measure", } @Article{Hajri:2014:SFM, author = "Hatem Hajri and Olivier Raimond", title = "Stochastic flows on metric graphs", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "12:1--12:20", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2773", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2773", abstract = "We study a simple stochastic differential equation driven by one Brownian motion on a general oriented metric graph whose solutions are stochastic flows of kernels. Under some condition, we describe the laws of all solutions. This work is a natural continuation of previous works by Hajri, Hajri--Raimond and Le Jan--Raimond where some particular graphs have been considered.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "metric graphs; Skew Brownian motion; stochastic flows of kernels; stochastic flows of mappings", } @Article{Bollobas:2014:BPG, author = "B{\'e}la Bollob{\'a}s and Karen Gunderson and Cecilia Holmgren and Svante Janson and Micha{\l} Przykucki", title = "Bootstrap percolation on {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "13:1--13:27", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2758", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2758", abstract = "Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number $r$, the $r$-neighbour bootstrap process is an update rule for vertices of a graph in one of two states: `infected' or `healthy'. In consecutive rounds, each healthy vertex with at least $r$ infected neighbours becomes itself infected. Percolation is said to occur if every vertex is eventually infected. Usually, the starting set of infected vertices is chosen at random, with all vertices initially infected independently with probability $p$. In that case, given a graph $G$ and infection threshold $r$, a quantity of interest is the critical probability, $ p_c(G, r)$, at which percolation becomes likely to occur. In this paper, we look at infinite trees and, answering a problem posed by Balogh, Peres and Pete, we show that for any $ b \geq r$ and for any $ \epsilon > 0$ there exists a tree $T$ with branching number $ \operatorname {br}(T) = b$ and critical probability $ p_c(T, r) < \epsilon $. However, this is false if we limit ourselves to the well studied family of Galton--Watson trees. We show that for every $ r \geq 2$ there exists a constant $ c_r > 0$ such that if $T$ is a Galton- Watson tree with branching number $ \operatorname {br}(T) = b \geq r$ then\par $$ p_c(T, r) > \frac {c_r}{b} e^{- \frac {b}{r - 1}}. $$ We also show that this bound is sharp up to a factor of $ O(b)$ by giving an explicit family of Galton--Watson trees with critical probability bounded from above by $ C_r e^{- \frac {b}{r - 1}}$ for some constant $ C_r > 0$.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bootstrap percolation; branching number; Galton--Watson trees; infinite trees", } @Article{Jahnel:2014:SDM, author = "Benedikt Jahnel and Christof K{\"u}lske", title = "Synchronization for discrete mean-field rotators", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "14:1--14:26", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2948", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2948", abstract = "We analyze a non-reversible mean-field jump dynamics for discrete q-valued rotators and show in particular that it exhibits synchronization. The dynamics is the mean-field analogue of the lattice dynamics investigated by the same authors which provides an example of a non-ergodic interacting particle system on the basis of a mechanism suggested by Maes and Shlosman.\par Based on the correspondence to an underlying model of continuous rotators via a discretization transformation we show the existence of a locally attractive periodic orbit of rotating measures. We also discuss global attractivity, using a free energy as a Lyapunov function and the linearization of the ODE which describes typical behavior of the empirical distribution vector.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "attractive limit cycle; clock model; discretization; Interacting particle systems; mean-field systems; non-equilibrium; rotation dynamics; synchronization; XY model", } @Article{Aldous:2014:SIR, author = "David Aldous", title = "Scale-invariant random spatial networks", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "15:1--15:41", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2920", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2920", abstract = "Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are exactly invariant under Euclidean scaling? This requires working in the continuum plane. We introduce an axiomatization of a class of processes we call ``scale-invariant random spatial networks'', whose primitives are routes between each pair of points in the plane. We prove that one concrete model, based on minimum-time routes in a binary hierarchy of roads with different speed limits, satisfies the axioms, and note informally that two other constructions (based on Poisson line processes and on dynamic proximity graphs) are expected also to satisfy the axioms. We initiate study of structure theory and summary statistics for general processes in this class.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Poisson process, scale invariance, spatial network", } @Article{Simon:2014:CFP, author = "Thomas Simon", title = "Comparing {Fr{\'e}chet} and positive stable laws", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "16:1--16:25", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3058", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3058", abstract = "Let $ {\bf L} $ be the unit exponential random variable and $ {\bf Z}_\alpha $ the standard positive $ \alpha $-stable random variable. We prove that $ \{ (1 - \alpha) \alpha^{\gamma_\alpha } {\bf Z}_\alpha^{- \gamma_\alpha }, 0 < \alpha < 1 \} $ is decreasing for the optimal stochastic order and that $ \{ (1 - \alpha){\bf Z}_\alpha^{ \gamma_\alpha }, 0 < \alpha < 1 \} $ is increasing for the convex order, with $ \gamma_\alpha = \alpha / (1 - \alpha).$ We also show that $ \{ \Gamma (1 + \alpha) {\bf Z}_\alpha^{- \alpha }, 1 / 2 \leq \alpha \leq 1 \} $ is decreasing for the convex order, that $ {\bf Z}_\alpha^{ \alpha } \, \prec_{st} \, \Gamma (1 - \alpha) {\bf L}$ and that $ \Gamma (1 + \alpha){\bf Z}_\alpha^{- \alpha } \, \prec_{cx} \, {\bf L}.$ This allows to compare $ {\bf Z}_\alpha $ with the two extremal Fr{\'e}chet distributions corresponding to the behaviour of its density at zero and at infinity. We also discuss the applications of these bounds to the strange behaviour of the median of $ {\bf Z}_\alpha $ and $ {\bf Z}_\alpha^{- \alpha }$ and to some uniform estimates on the classical Mittag-Leffler function. Along the way, we obtain a canonical factorization of $ {\bf Z}_\alpha $ for $ \alpha $ rational in terms of Beta random variables. The latter extends to the one-sided branches of real strictly stable densities.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Convex order; Fr{\'e}chet distribution; Median; Mittag-Leffler distribution; Mittag-Leffler function; stable distribution; stochastic order", } @Article{Li:2014:LBD, author = "Xinyi Li and Alain-Sol Sznitman", title = "A lower bound for disconnection by random interlacements", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "17:1--17:26", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3067", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3067", abstract = "We consider the vacant set of random interlacements on $ \mathbb {Z}^d $, with $d$ bigger or equal to 3, in the percolative regime. Motivated by the large deviation principles obtained in our recent work arXiv:1304.7477, we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the random interlacements. We derive an asymptotic lower bound, which brings into play tilted interlacements, and relates the problem to some of the large deviations of the occupation-time profile considered in arXiv:1304.7477.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "disconnection; large deviations; random interlacements", } @Article{Bovier:2014:EPT, author = "Anton Bovier and Lisa Hartung", title = "The extremal process of two-speed branching {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "18:1--18:28", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2982", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2982", abstract = "We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is $ \sigma_1 $ for $ s \leq b t $ and $ \sigma_2 $ when $ b t \leq s \leq t $. In the case $ \sigma_1 > \sigma_2 $, the process is the concatenation of two BBM extremal processes, as expected. In the case $ \sigma_1 < \sigma_2 $, a new family of cluster point processes arises, that are similar, but distinctively different from the BBM process. Our proofs follow the strategy of Arguin, Bovier, and Kistler.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching Brownian motion, extremal processes, extreme values, F-KPP equation, cluster point processes", } @Article{Haggstrom:2014:FRC, author = "Olle H{\"a}ggstr{\"o}m and Timo Hirscher", title = "Further results on consensus formation in the {Deffuant} model", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "19:1--19:26", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3116", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3116", abstract = "The so-called Deffuant model describes a pattern for social interaction, in which two neighboring individuals randomly meet and share their opinions on a certain topic, if their discrepancy is not beyond a given threshold $ \theta $. The major focus of the analyses, both theoretical and based on simulations, lies on whether these single interactions lead to a global consensus in the long run or not. First, we generalize a result of Lanchier for the Deffuant model on $ \mathbb {Z} $, determining the critical value for $ \theta $ at which a phase transition of the long term behavior takes place, to other distributions of the initial opinions than i.i.d. uniform on $ [0, 1] $. Then we shed light on the situations where the underlying line graph $ \mathbb {Z} $ is replaced by higher-dimensional lattices $ \mathbb {Z}^d, \ d \geq 2 $, or the infinite cluster of supercritical i.i.d. bond percolation on these lattices.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Deffuant model, consensus formation, percolation", } @Article{Bordenave:2014:EPT, author = "Charles Bordenave", title = "Extinction probability and total progeny of predator-prey dynamics on infinite trees", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "20:1--20:33", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2361", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2361", abstract = "We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This model was defined as the chase-escape model by Kordzakhia and it admits a limit process, the birth-and-assassination process, previously introduced by Aldous and Krebs. On both models, we prove an asymptotic equivalent of the extinction probability near criticality. In the subcritical regime, we give a tail bound on the total progeny of the preys before extinction.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "SIR models, predator-prey dynamics, branching processes", } @Article{Favaro:2014:ANB, author = "Stefano Favaro and Shui Feng", title = "Asymptotics for the number of blocks in a conditional {Ewens--Pitman} sampling model", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "21:1--21:15", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2881", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2881", abstract = "The study of random partitions has been an active research area in probability over the last twenty years. A quantity that has attracted a lot of attention is the number of blocks in the random partition. Depending on the area of applications this quantity could represent the number of species in a sample from a population of individuals or he number of cycles in a random permutation, etc. In the context of Bayesian nonparametric inference such a quantity is associated with the exchangeable random partition induced by sampling from certain prior models, for instance the Dirichlet process and the two parameter Poisson--Dirichlet process. In this paper we generalize some existing asymptotic results from this prior setting to the so-called posterior, or conditional, setting. Specifically, given an initial sample from a two parameter Poisson--Dirichlet process, we establish conditional fluctuation limits and conditional large deviation principles for the number of blocks generated by a large additional sample.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Bayesian nonparametrics; Dirichlet process; Ewens--Pitman sampling model; exchangeable random partition; fluctuation limit; large deviations; two parameter Poisson--Dirichlet process", } @Article{Berard:2014:LPP, author = "Jean B{\'e}rard and Pascal Maillard", title = "The limiting process of {$N$}-particle branching random walk with polynomial tails", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "22:1--22:17", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3111", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3111", abstract = "We consider a system of $N$ particles on the real line that evolves through iteration of the following steps: (1) every particle splits into two, (2) each particle jumps according to a prescribed displacement distribution supported on the positive reals and (3) only the $N$ right most particles are retained, the others being removed from the system. This system has been introduced in the physics literature as an example of a microscopic stochastic model describing the propagation of a front. Its behavior for large $N$ is now well understood --- both from a physical and mathematical viewpoint --- in the case where the displacement distribution admits exponential moments. Here, we consider the case of displacements with regularly varying tails, where the relevant space and time scales are markedly different. We characterize the behavior of the system for two distinct asymptotic regimes. First, we prove convergence in law of the rescaled positions of the particles on a time scale of order $ \log N$ and give a construction of the limit based on the records of a space time Poisson point process. Second, we determine the appropriate scaling when we let first the time horizon, then $N$ go to infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching random walk; heavy-tailed distribution; selection", } @Article{Otto:2014:IMS, author = "Felix Otto and Hendrik Weber and Maria Westdickenberg", title = "Invariant measure of the stochastic {Allen--Cahn} equation: the regime of small noise and large system size", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "23:1--23:76", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2813", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2813", abstract = "We study the invariant measure of the one-dimensional stochastic Allen Cahn equation for a small noise strength and a large but finite system with so-called Dobrushin boundary conditions, i.e., inhomogeneous $ \pm 1 $ Dirichlet boundary conditions that enforce at least one transition layer from $ - 1 $ to $1$. (Our methods can be applied to other boundary conditions as well.) We are interested in the competition between the ``energy'' that should be minimized due to the small noise strength and the ``entropy'' that is induced by the large system size.\par Specifically, in the context of system sizes that are exponential with respect to the inverse noise strength---up to the ``critical'' exponential size predicted by the heuristics---we study the extremely strained large deviation event of seeing \emph{more than the one transition layer} between $ \pm 1$ that is forced by the boundary conditions. We capture the competition between energy and entropy through upper and lower bounds on the probability of these unlikely extra transition layers. Our bounds are sharp on the exponential scale and imply in particular that the probability of having one and only one transition from $ - 1$ to $ + 1$ is exponentially close to one. Our second result then studies the distribution of the transition layer. In particular, we establish that, on a super-logarithmic scale, the position of the transition layer is approximately uniformly distributed.\par In our arguments we use local large deviation bounds, the strong Markov property, the symmetry of the potential, and measure-preserving reflections.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "invariant measure; large deviations; stochastic partial differential equation", } @Article{Bertoin:2014:NGF, author = "Jean Bertoin", title = "On the non-{Gaussian} fluctuations of the giant cluster for percolation on random recursive trees", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "24:1--24:15", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2822", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2822", abstract = "We consider a Bernoulli bond percolation on a random recursive tree of size $ n \gg 1 $, with supercritical parameter $ p_n = 1 - c / \ln n $ for some $ c > 0 $ fixed. It is known that with high probability, there exists then a unique giant cluster of size $ G_n \sim e^{-c}n $, and it follows from a recent result of Schweinsberg that $ G_n $ has non-Gaussian fluctuations. We provide an explanation of this by analyzing the effect of percolation on different phases of the growth of recursive trees. This alternative approach may be useful for studying percolation on other classes of trees, such as for instance regular trees.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random recursive tree, giant cluster, fluctuations, super-critical percolation", } @Article{Kosygina:2014:EER, author = "Elena Kosygina and Martin Zerner", title = "Excursions of excited random walks on integers", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "25:1--25:25", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2940", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2940", abstract = "Several phase transitions for excited random walks on the integers are known to be characterized by a certain drift parameter $ \delta \in \mathbb R $. For recurrence/transience the critical threshold is $ | \delta | = 1 $, for ballisticity it is $ | \delta | = 2 $ and for diffusivity $ | \delta | = 4 $. In this paper we establish a phase transition at $ | \delta | = 3 $. We show that the expected return time of the walker to the starting point, conditioned on return, is finite iff $ | \delta | > 3 $. This result follows from an explicit description of the tail behaviour of the return time as a function of $ \delta $, which is achieved by diffusion approximation of related branching processes by squared Bessel processes.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "branching process, cookie walk, diffusion approximation, excited random walk, excursion, squared Bessel process, return time, strong transience", } @Article{Basdevant:2014:SLB, author = "Anne-Laure Basdevant and Nathana{\"e}l Enriquez and Lucas Gerin and Jean-Baptiste Gou{\'e}r{\'e}", title = "The shape of large balls in highly supercritical percolation", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "26:1--26:14", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3062", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3062", abstract = "We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on Z. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "first-passage percolation; supercritical percolation; TASEP", } @Article{Tropp:2014:SMP, author = "Joel Tropp and Richard Chen", title = "Subadditivity of matrix phi-entropy and concentration of random matrices", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "27:1--27:30", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2964", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2964", abstract = "This paper considers a class of entropy functionals defined for random matrices, and it demonstrates that these functionals satisfy a subadditivity property. Several matrix concentration inequalities are derived as an application of this result.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Entropy; inequalities; large deviations; random matrices", } @Article{Durrett:2014:CPF, author = "Rick Durrett and Thomas Liggett and Yuan Zhang", title = "The contact process with fast voting", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "28:1--28:19", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3021", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3021", abstract = "Consider a combination of the contact process and the voter model in which deaths occur at rate 1 per site, and across each edge between nearest neighbors births occur at rate $ \lambda $ and voting events occur at rate $ \theta $. We are interested in the asymptotics as $ \theta \to \infty $ of the critical value $ \lambda_c(\theta) $ for the existence of a nontrivial stationary distribution. In $ d \ge 3 $, $ \lambda_c(\theta) \to 1 / (2 d \rho_d) $ where $ \rho_d $ is the probability a $d$ dimensional simple random walk does not return to its starting point. In $ d = 2$, $ \lambda_c(\theta) / \log (\theta) \to 1 / 4 \pi $, while in $ d = 1$, $ \lambda_c(\theta) / \theta^{1 / 2}$ has $ \liminf \ge 1 / \sqrt {2}$ and $ \limsup < \infty $. The lower bound might be the right answer, but proving this, or even getting a reasonable upper bound, seems to be a difficult problem.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "contact process, voter model, block construction", } @Article{Jourdain:2014:SNL, author = "Benjamin Jourdain and Julien Reygner", title = "The small noise limit of order-based diffusion processes", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "29:1--29:36", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2906", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2906", abstract = "In this article, we introduce and study order-based diffusion processes. They are the solutions to multidimensional stochastic differential equations with constant diffusion matrix, proportional to the identity, and drift coefficient depending only on the ordering of the coordinates of the process. These processes describe the evolution of a system of Brownian particles moving on the real line with piecewise constant drifts, and are the natural generalization of the rank-based diffusion processes introduced in stochastic portfolio theory or in the probabilistic interpretation of nonlinear evolution equations. Owing to the discontinuity of the drift coefficient, the corresponding ordinary differential equations are ill-posed. Therefore, the small noise limit of order-based diffusion processes is not covered by the classical Freidlin--Wentzell theory. The description of this limit is the purpose of this article.\par We first give a complete analysis of the two-particle case. Despite its apparent simplicity, the small noise limit of such a system already exhibits various behaviours. In particular, depending on the drift coefficient, the particles can either stick into a cluster, the velocity of which is determined by elementary computations, or drift away from each other at constant velocity, in a random ordering. The persistence of randomness in the small noise limit is of the very same nature as in the pioneering works by Veretennikov (Mat. Zametki, 1983) and Bafico and Baldi (Stochastics, 1981) concerning the so-called Peano phenomenon.\par In the case of rank-based processes, we use a simple convexity argument to prove that the small noise limit is described by the sticky particle dynamics introduced by Brenier and Grenier (SIAM J. Numer. Anal., 1998), where particles travel at constant velocity between collisions, at which they stick together. In the general case of order-based processes, we give a sufficient condition on the drift for all the particles to aggregate into a single cluster, and compute the velocity of this cluster. Our argument consists in turning the study of the small noise limit into the study of the long time behaviour of a suitably rescaled process, and then exhibiting a Lyapunov functional for this rescaled process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Lyapunov functional; Order-based diffusion process; Peano phenomenon; small noise; sticky particle dynamics", } @Article{Kuznetsov:2014:HTZ, author = "Alexey Kuznetsov and Andreas Kyprianou and Juan Carlos Pardo and Alexander Watson", title = "The hitting time of zero for a stable process", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "30:1--30:26", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2647", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2647", abstract = "For any two-sided jumping $ \alpha $-stable process, where $ 1 < \alpha < 2$, we find an explicit identity for the law of the first hitting time of the origin. This complements existing work in the symmetric case and the spectrally one-sided case; cf. Yano--Yano--Yor (2009) and Cordero (2010), and Peskir (2008) respectively. We appeal to the Lamperti--Kiu representation of Chaumont--Panti--Rivero (2011) for real-valued self similar Markov processes. Our main result follows by considering a vector-valued functional equation for the Mellin transform of the integrated exponential Markov additive process in the Lamperti--Kiu representation. We conclude our presentation with some applications.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Levy processes, stable processes, positive self-similar Markov processes", } @Article{Bjornberg:2014:RBP, author = "Jakob Bj{\"o}rnberg and Sigurdur Stef{\'a}nsson", title = "Recurrence of bipartite planar maps", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "31:1--31:40", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3102", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3102", abstract = "This paper concerns random bipartite planar maps which are defined by assigning weights to their faces. The paper presents a threefold contribution to the theory. Firstly, we prove the existence of the local limit for all choices of weights and describe it in terms of an infinite mobile. Secondly, we show that the local limit is in all cases almost surely recurrent. And thirdly, we show that for certain choices of weights the local limit has exactly one face of infinite degree and has in that case spectral dimension 4/3 (the latter requires a mild moment condition).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "local limits; Planar maps; random walk; simply generated trees", } @Article{Bass:2014:SDE, author = "Richard Bass", title = "A stochastic differential equation with a sticky point", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "32:1--32:22", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2350", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2350", abstract = "We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution exist.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion; diffusions; sticky point; stochastic differential equations", } @Article{Alex:2014:ILL, author = "Bloemendal Alex and L{\'a}szl{\'o} Erd{\H{o}}s and Antti Knowles and Horng-Tzer Yau and Jun Yin", title = "Isotropic local laws for sample covariance and generalized {Wigner} matrices", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "33:1--33:53", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3054", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3054", abstract = "We consider sample covariance matrices of the form $ X^*X $, where $X$ is an $ M \times N$ matrix with independent random entries. We prove the isotropic local Marchenko--Pastur law, i.e., we prove that the resolvent $ (X^* X - z)^{-1}$ converges to a multiple of the identity in the sense of quadratic forms. More precisely, we establish sharp high-probability bounds on the quantity $ \langle v, (X^* X - z)^{-1}w \rangle - \langle v, w \rangle m(z)$, where $m$ is the Stieltjes transform of the Marchenko--Pastur law and $ v, w \in \mathbb {C}^N$. We require the logarithms of the dimensions $M$ and $N$ to be comparable. Our result holds down to scales $ \Im z \geq N^{-1 + \varepsilon }$ and throughout the entire spectrum away from 0. We also prove analogous results for generalized Wigner matrices.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Sosoe:2014:CED, author = "Philippe Sosoe and Percy Wong", title = "Convergence of the eigenvalue density for {Laguerre} beta ensembles on short scales", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "34:1--34:18", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2638", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2638", abstract = "In this note, we prove that the normalized trace of the resolvent of the beta-Laguerre ensemble eigenvalues is close to the Stieltjes transform of the Marchenko--Pastur (MP) distribution with very high probability, for values of the imaginary part greater than $ m^{1 + \varepsilon } $. As an immediate corollary, we obtain convergence of the one-point density to the MP law on short scales. The proof serves to illustrate some simplifications of the method introduced in our previous work to prove a local semi-circle law for Gaussian beta-ensembles.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Ranbom Matrices, Beta Ensembles, Marchenko--Pastur law", } @Article{Coupier:2014:CPQ, author = "David Coupier and David Dereudre", title = "Continuum percolation for {Quermass} model", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "35:1--35:19", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2298", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2298", abstract = "The continuum percolation for Markov (or Gibbs) germ-grain models is investigated. The grains are assumed circular with random radii on a compact support. The morphological interaction is the so-called Quermass interaction defined by a linear combination of the classical Minkowski functionals (area, perimeter and Euler--Poincar{\'e} characteristic). We show that the percolation occurs for any coefficient of this linear combination and for a large enough activity parameter. An application to the phase transition of the multi-type quermass model is given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic geometry, Gibbs point process, germ-grain model, Quermass interaction, percolation, phase transition", } @Article{Alili:2014:MLT, author = "Larbi Alili and Ching-Tang Wu", title = "{M{\"u}ntz} linear transforms of {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "36:1--36:15", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2424", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2424", abstract = "We consider a class of Volterra linear transforms of Brownian motion associated to a sequence of M{\"u}ntz Gaussian spaces and determine explicitly their kernels; the kernels take a simple form when expressed in terms of M{\"u}ntz-Legendre polynomials. These are new explicit examples of progressive Gaussian enlargement of a Brownian filtration. We give a necessary and sufficient condition for the existence of kernels of infinite order associated to an infinite dimensional M{\"u}ntz Gaussian space; we also examine when the transformed Brownian motion remains a semimartingale in the filtration of the original process. This completes some already obtained partial answers to the aforementioned problems in the infinite dimensional case.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Enlargement of filtration; Gaussian process; noncanonical representation; self-reproducing kernel; M{\"u}ntz polynomials; Volterra representation", } @Article{Elie:2014:ENB, author = "Romuald Elie and Mathieu Rosenbaum and Marc Yor", title = "On the expectation of normalized {Brownian} functionals up to first hitting times", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "37:1--37:23", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3049", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3049", abstract = "Let $B$ be a Brownian motion and $ T_1$ its first hitting time of the level $1$. For $U$ a uniform random variable independent of $B$, we study in depth the distribution of $ B_{UT_1} / \sqrt {T_1}$, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion, hitting times, scaling, random sampling, Bessel process, Brownian meander, Ray--Knight theorem, Feynman--Kac formula", } @Article{Gaunt:2014:VGA, author = "Robert Gaunt", title = "Variance-{Gamma} approximation via {Stein}'s method", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "38:1--38:33", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3020", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3020", abstract = "Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a Stein equation and smoothness estimates for its solution. This Stein equation has the attractive property of reducing to the known normal and Gamma Stein equations for certain parameter values. We apply these results and local couplings to bound the distance between sums of the form $ \sum_{i, j, k = 1}^{m, n, r}X_{ik}Y_{jk} $, where the $ X_{ik} $ and $ Y_{jk} $ are independent and identically distributed random variables with zero mean, by their limiting Variance-Gamma distribution. Through the use of novel symmetry arguments, we obtain a bound on the distance that is of order $ m^{-1} + n^{-1} $ for smooth test functions. We end with a simple application to binary sequence comparison.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "rates of convergence; Stein's method; Variance-Gamma approximation", } @Article{Chazottes:2014:TFL, author = "Jean-Ren{\'e} Chazottes and Frank Redig", title = "Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "39:1--39:19", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3189", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3189", abstract = "We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional `layer-unique' Gibbs measures for which the same results can be obtained. For more general models associated to a $d$-dimensional multiplicative invariant potential, we prove a large deviation theorem in the uniqueness regime for averages of multiplicative shifts of general local functions. This thermodynamic formalism is motivated by the statistical properties of multiple ergodic averages.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Monter:2014:IDF, author = "Sergio Almada Monter and Amarjit Budhiraja", title = "Infinite dimensional forward--backward stochastic differential equations and the {KPZ} equation", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "40:1--40:21", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2709", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2709", abstract = "Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation (SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of this equation. Bertini, Cancrini and Giacomin have proposed a notion of a solution through a limiting procedure and a certain renormalization of the nonlinearity. In this work we study connections between the KPZ equation and certain infinite dimensional forward--backward stochastic differential equations. Forward-backward equations with a finite dimensional noise have been studied extensively, mainly motivated by problems in mathematical finance. Equations considered here differ from the classical works in that, in addition to having an infinite dimensional driving noise, the associated SPDE involves a non-Lipschitz (specifically, a quadratic) function of the gradient. Existence and uniqueness of solutions of such infinite dimensional forward--backward equations is established and the terminal values of the solutions are then used to give a new probabilistic representation for the solution of the KPZ equation.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "KPZ Equation, Backward SDE, Feynman--Kac", } @Article{Su:2014:BRW, author = "Wei Su", title = "Branching random walks and contact processes on {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "41:1--41:12", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3118", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3118", abstract = "We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is a Galton--Watson tree then, in certain circumstances, the branching random walks and contact processes will have weak survival phases. We also provide bounds on critical values.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Branching Random Walk; Contact Process; Galton--Watson Tree; Phase Transition", } @Article{Andreoletti:2014:SVS, author = "Pierre Andreoletti and Pierre Debs", title = "Spread of visited sites of a random walk along the generations of a branching process", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "42:1--42:22", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2790", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2790", abstract = "In this paper we consider a null recurrent random walk in random environment on a super-critical Galton--Watson tree. We consider the case where the log-Laplace transform $ \psi $ of the branching process satisfies $ \psi (1) = \psi '(1) = 0 $ for which G. Faraud, Y. Hu and Z. Shi have shown that, with probability one, the largest generation visited by the walk, until the instant $n$, is of the order of $ (\log n)^3$. We already proved that the largest generation entirely visited behaves almost surely like $ \log n$ up to a constant. Here we study how the walk visits the generations $ \ell = (\log n)^{1 + \zeta }$, with $ 0 < \zeta < 2$. We obtain results in probability giving the asymptotic logarithmic behavior of the number of visited sites at a given generation. We prove that there is a phase transition at generation $ (\log n)^2$ for the mean of visited sites until $n$ returns to the root. Also we show that the visited sites spread all over the tree until generation $ \ell $.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "random walks, random environment, trees, branching random walk", } @Article{ORourke:2014:LRP, author = "Sean O'Rourke and David Renfrew", title = "Low rank perturbations of large elliptic random matrices", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "43:1--43:65", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3057", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3057", abstract = "We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and non-Hermitian random matrices with iid entries. As a consequence, we recover the results of Capitaine, Donati-Martin, and F{\'e}ral for perturbed Wigner matrices as well as the results of Tao for perturbed random matrices with iid entries. Along the way, we prove a number of interesting results concerning elliptic random matrices whose entries have finite fourth moment; these results include a bound on the least singular value and the asymptotic behavior of the spectral radius.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "elliptic random matrix; low rank perturbation; Wigner matrix", } @Article{Denis:2014:MPQ, author = "Laurent Denis and Anis Matoussi and Jing Zhang", title = "Maximum principle for quasilinear stochastic {PDEs} with obstacle", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "44:1--44:32", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2716", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2716", abstract = "We prove a maximum principle for local solutions of quasi linear stochastic PDEs with obstacle (in short OSPDE). The proofs are based on a version of It{\^o}'s formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Stochastic PDE's, Obstacle problems, It{\^o}'s formula, $L^p-$estimate, Local solution, Comparison theorem, Maximum principle, Moser iteration", } @Article{Eldan:2014:VPC, author = "Ronen Eldan", title = "Volumetric properties of the convex hull of an $n$-dimensional {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "45:1--45:34", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2571", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2571", abstract = "Let $K$ be the convex hull of the path of a standard brownian motion $ B(t)$ in $ R^n$, taken at time $ 0 < t < 1$. We derive formulas for the expected volume and surface area of $K$. Moreover, we show that in order to approximate $K$ by a discrete version of $K$, namely by the convex hull of a random walk attained by taking $ B(t_n)$ at discrete (random) times, the number of steps that one should take in order for the volume of the difference to be relatively small is of order $ n^3$. Next, we show that the distribution of facets of $K$ is in some sense scale invariant: for any given family of simplices (satisfying some compactness condition), one expects to find in this family a constant number of facets of $ t K$ as $t$ approaches infinity. Finally, we discuss some possible extensions of our methods and suggest some further research.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Vollering:2014:VIG, author = "Florian V{\"o}llering", title = "A variance inequality for {Glauber} dynamics applicable to high and low temperature regimes", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "46:1--46:21", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2791", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2791", abstract = "A variance inequality for spin-flip systems is obtained using comparatively weaker knowledge of relaxation to equilibrium based on coupling estimates for single site disturbances. We obtain variance inequalities interpolating between the Poincar{\'e} inequality and the uniform variance inequality, and a general weak Poincar{\'e} inequality. For monotone dynamics the variance inequality can be obtained from decay of the autocorrelation of the spin at the origin i.e., from that decay we conclude decay for general functions. This method is then applied to the low temperature Ising model, where the time-decay of the autocorrelation of the origin is extended to arbitrary quasi-local functions.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Glauber dynamics, weak Poincare inequality, relaxation to equilibrium, coupling", } @Article{Ray:2014:GPH, author = "Gourab Ray", title = "Geometry and percolation on half planar triangulations", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "47:1--47:28", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3238", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3238", abstract = "We analyze the geometry of domain Markov half planar triangulations. In [5] it is shown that there exists a one-parameter family of measures supported on half planar triangulations satisfying translation invariance and domain Markov property. We study the geometry of these maps and show that they exhibit a sharp phase-transition in view of their geometry at $ \alpha = 2 / 3 $. For $ \alpha < 2 / 3 $, the maps form a tree-like stricture with infinitely many small cut-sets. For $ \alpha > 2 / 3 $, we obtain maps of hyperbolic nature with exponential growth and anchored expansion. Some results about the geometry of percolation clusters on such maps and random walk on them are also obtained.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "half planar maps, volume growth, anchored expansion, percolation", } @Article{Li:2014:MDC, author = "Zhongyang Li", title = "1-2 model, dimers and clusters", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "48:1--48:28", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2563", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2563", abstract = "The 1-2 model is a probability measure on subgraphs of the hexagonal lattice, satisfying the condition that the degree of present edges at each vertex is either 1 or 2. We prove that for any translation-invariant Gibbs measure of the 1-2 model on the plane, almost surely there are no infinite paths. Using a measure-preserving correspondence between 1-2 model configurations on the hexagonal lattice and perfect matchings on a decorated graph, we construct an explicit translation-invariant measure $P$ for 1-2 model configurations on the bi-periodic hexagonal lattice embedded into the whole plane. We prove that the behavior of infinite clusters is different for small and large local weights, which shows the existence of a phase transition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{dosSantos:2014:NTL, author = "Renato Soares dos Santos", title = "Non-trivial linear bounds for a random walk driven by a simple symmetric exclusion process", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "49:1--49:18", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3159", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3159", abstract = "Linear bounds are obtained for the displacement of a random walk in a dynamic random environment given by a one-dimensional simple symmetric exclusion process in equilibrium. The proof uses an adaptation of multiscale renormalization methods of Kesten and Sidoravicius.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walk, dynamic random environment, exclusion process, linear bounds, multiscale analysis, percolation", } @Article{Luschgy:2014:CQF, author = "Harald Luschgy and Gilles Pag{\`e}s", title = "Constructive quadratic functional quantization and critical dimension", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "50:1--50:19", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3010", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3010", abstract = "We propose a constructive proof for the sharp rate of optimal quadratic functional quantization and we tackle the asymptotics of the critical dimension for quadratic functional quantization of Gaussian stochastic processes as the quantization level goes to infinity, i.e., the smallest dimensional truncation of an optimal quantization of the process which is `fully' quantized. We first establish a lower bound for this critical dimension based on the regular variation index of the eigenvalues of the Karhunen--Lo{\`e}ve expansion of the process. This lower bound is consistent with the commonly shared sharp rate conjecture (and supported by extensive numerical experiments). Moreover, we show that, conversely, optimized quadratic functional quantizations based on this critical dimension rate are always asymptotically optimal (strong admissibility result).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "asymptotically optimal quantizer; Gaussian process; Karhunen--Lo{\`e}ve expansion; optimal quantizer; quadratic functional quantization; Shannon's entropy", } @Article{Filipovic:2014:IMB, author = "Damir Filipovi{\'c} and Stefan Tappe and Josef Teichmann", title = "Invariant manifolds with boundary for jump-diffusions", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "51:1--51:28", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2882", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2882", abstract = "We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Spinka:2014:RWL, author = "Yinon Spinka and Ron Peled", title = "Random walk with long-range constraints", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "52:1--52:54", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3060", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3060", abstract = "We consider a model of a random height function with long-range constraints on a discrete segment. This model was suggested by Benjamini, Yadin and Yehudayoff and is a generalization of simple random walk. The random function is uniformly sampled from all graph homomorphisms from the graph $ P_{n, d} $ to the integers $ \mathbb {Z} $, where the graph $ P_{n, d} $ is the discrete segment $ \{ 0, 1, \ldots, n \} $ with edges between vertices of different parity whose distance is at most $ 2 d + 1 $. Such a graph homomorphism can be viewed as a height function whose values change by exactly one along edges of the graph $ P_{n, d} $. We also consider a similarly defined model on the discrete torus.\par Benjamini, Yadin and Yehudayoff conjectured that this model undergoes a phase transition from a delocalized to a localized phase when $d$ grows beyond a threshold $ c \log n$. We establish this conjecture with the precise threshold $ \log_2 n$. Our results provide information on the typical range and variance of the height function for every given pair of $n$ and $d$, including the critical case when $ d - \log_2 n$ tends to a constant.\par In addition, we identify the local limit of the model, when $d$ is constant and $n$ tends to infinity, as an explicitly defined Markov chain.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random walk, random graph homomorphism, phase transition, Lipschitz function", } @Article{Sturm:2014:SCP, author = "Anja Sturm and Jan Swart", title = "Subcritical contact processes seen from a typical infected site", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "53:1--53:46", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2904", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2904", abstract = "What is the long-time behavior of the law of a contact process started with a single infected site, distributed according to counting measure on the lattice? This question is related to the configuration as seen from a typical infected site and gives rise to the definition of so-called eigenmeasures, which are possibly infinite measures on the set of nonempty configurations that are preserved under the dynamics up to a time-dependent exponential factor. In this paper, we study eigenmeasures of contact processes on general countable groups in the subcritical regime. We prove that in this regime, the process has a unique spatially homogeneous eigenmeasure. As an application, we show that the law of the process as seen from a typical infected site, chosen according to a Campbell law, converges to a long-time limit. We also show that the exponential decay rate of the expected number of infected sites is continuously differentiable and strictly increasing as a function of the recovery rate, and we give a formula for the derivative in terms of the long time limit law of the process as seen from a typical infected site.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Contact process, exponential growth rate, eigenmeasure, Campbell law, Palm law, quasi-invariant law", } @Article{Benaych-Georges:2014:CLT, author = "Florent Benaych-Georges and Alice Guionnet", title = "Central limit theorem for eigenvectors of heavy tailed matrices", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "54:1--54:27", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3093", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3093", abstract = "We consider the eigenvectors of symmetric matrices with independent heavy tailed entries, such as matrices with entries in the domain of attraction of $ \alpha $-stable laws, or adjacency matrices of Erd{\H{o}}s--R{\'e}nyi graphs. We denote by $ U = [u_{ij}]$ the eigenvectors matrix (corresponding to increasing eigenvalues) and prove that the bivariate process\par $$ B^n_{s, t} := n^{-1 / 2} \sum_{1 \leq i \leq ns, 1 \leq j \leq nt}(|u_{ij}|^2 - n^{-1}), $$ indexed by $ s, t \in [0, 1]$, converges in law to a non trivial Gaussian process. An interesting part of this result is the $ n^{-1 / 2}$ rescaling, proving that from this point of view, the eigenvectors matrix $U$ behaves more like a permutation matrix (as it was proved by Chapuy that for $U$ a permutation matrix, $ n^{-1 / 2}$ is the right scaling) than like a Haar-distributed orthogonal or unitary matrix (as it was proved by Rouault and Donati-Martin that for $U$ such a matrix, the right scaling is $1$).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random matrices, heavy tailed random variables, eigenvectors, central limit theorem", } @Article{Labbe:2014:FFV, author = "Cyril Labb{\'e}", title = "From flows of {$ \Lambda $}-{Fleming--Viot} processes to lookdown processes via flows of partitions", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "55:1--55:49", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3192", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3192", abstract = "The goal of this paper is to unify the lookdown representation and the stochastic flow of bridges, which are two approaches to construct the $ \Lambda $-Fleming--Viot process along with its genealogy. First we introduce the stochastic flow of partitions and show that it provides a new formulation of the lookdown representation. Second we study the asymptotic behaviour of the $ \Lambda $-Fleming--Viot process and we provide sufficient conditions for the existence of an infinite sequence of Eves that generalise the primitive Eve of Bertoin and Le Gall. Finally under the condition that this infinite sequence of Eves does exist, we construct the lookdown representation pathwise from a flow of bridges.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Coalescent; Exchangeable bridge; Fleming--Viot process; Lookdown process; Partition; Stochastic flow", } @Article{Abraham:2014:LLCb, author = "Romain Abraham and Jean-Fran{\c{c}}ois Delmas", title = "Local limits of conditioned {Galton--Watson} trees: the condensation case", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "56:1--56:29", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3164", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3164", abstract = "We provide a complete picture of the local convergence of critical or subcritical Galton--Watson tree conditioned on having a large number of individuals with out-degree in a given set. The generic case, where the limit is a random tree with an infinite spine has been treated in a previous paper. We focus here on the non-generic case, where the limit is a random tree with a node with infinite out-degree. This case corresponds to the so-called condensation phenomenon.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Galton--Watson, random tree, condensation, non-extinction, branching process", } @Article{Eckhoff:2014:VRP, author = "Maren Eckhoff and Peter M{\"o}rters", title = "Vulnerability of robust preferential attachment networks", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "57:1--57:47", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2974", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2974", abstract = "Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the science literature that such networks are highly vulnerable to a targeted attack, and removing a small number of key nodes in the network will dramatically change the topological structure. Here we analyse a class of preferential attachment networks in the robust regime and prove four main results supporting this claim: After removal of an arbitrarily small proportion $ \varepsilon > 0 $ of the oldest nodes (1) the asymptotic degree distribution has exponential instead of power law tails; (2) the largest degree in the network drops from being of the order of a power of the network size $n$ to being just logarithmic in $n$; (3) the typical distances in the network increase from order $ \log \log n$ to order $ \log n$; and (4) the network becomes vulnerable to random removal of nodes. Importantly, all our results explicitly quantify the dependence on the proportion $ \varepsilon $ of removed vertices. For example, we show that the critical proportion of nodes that have to be retained for survival of the giant component undergoes a steep increase as $ \varepsilon $ moves away from zero, and a comparison of this result with similar ones for other networks reveals the existence of two different universality classes of robust network models. The key technique in our proofs is a local approximation of the network by a branching random walk with two killing boundaries, and an understanding of the particle genealogies in this process, which enters into estimates for the spectral radius of an associated operator.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Power law, small world, scale-free network, preferential attachment, Barab{\'a}si-Albert model, percolation, maximal degree, diameter, network distance, robustness, vulnerability, multitype branching process, killed branching random walk", } @Article{Fiodorov:2014:CLE, author = "Artiom Fiodorov and Stephen Muirhead", title = "Complete localisation and exponential shape of the parabolic {Anderson} model with {Weibull} potential field", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "58:1--58:27", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3203", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3203", abstract = "We consider the parabolic Anderson model with Weibull potential field, for all values of the Weibull parameter. We prove that the solution is eventually localised at a single site with overwhelming probability (complete localisation) and, moreover, that the solution has exponential shape around the localisation site. We determine the localisation site explicitly, and derive limit formulae for its distance, the profile of the nearby potential field and its ageing behaviour. We also prove that the localisation site is determined locally, that is, by maximising a certain time-dependent functional that depends only on: (i) the value of the potential field in a neighbourhood of fixed radius around a site; and (ii) the distance of that site to the origin. Our results extend the class of potential field distributions for which the parabolic Anderson model is known to completely localise; previously, this had only been established in the case where the potential field distribution has sub-Gaussian tail decay, corresponding to a Weibull parameter less than two.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Anderson Hamiltonian; intermittency; localisation; Parabolic Anderson model; random Schrodinger operator; spectral gap; Weibull tail", } @Article{Gupta:2014:SAS, author = "Ankit Gupta and Mustafa Khammash", title = "Sensitivity analysis for stochastic chemical reaction networks with multiple time-scales", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "59:1--59:53", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3246", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3246", abstract = "Stochastic models for chemical reaction networks have become very popular in recent years. For such models, the estimation of parameter sensitivities is an important and challenging problem. Sensitivity values help in analyzing the network, understanding its robustness properties and also in identifying the key reactions for a given outcome. Most of the methods that exist in the literature for the estimation of parameter sensitivities, rely on Monte Carlo simulations using Gillespie's stochastic simulation algorithm or its variants. It is well-known that such simulation methods can be prohibitively expensive when the network contains reactions firing at different time-scales, which is a feature of many important biochemical networks. For such networks, it is often possible to exploit the time-scale separation and approximately capture the original dynamics by simulating a `reduced' model, which is obtained by eliminating the fast reactions in a certain way. The aim of this paper is to tie these model reduction techniques with sensitivity analysis. We prove that under some conditions, the sensitivity values for the reduced model can be used to approximately recover the sensitivity values for the original model. Through an example we illustrate how our result can help in sharply reducing the computational costs for the estimation of parameter sensitivities for reaction networks with multiple time-scales. To prove our result, we use coupling arguments based on the random time change representation of Kurtz. We also exploit certain connections between the distributions of the occupation times of Markov chains and multi-dimensional wave equations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "chemical reaction network; coupling; multiscale network; parameter sensitivity; random time change; reduced models; time-scale separation", } @Article{Fitzsimmons:2014:MLS, author = "Patrick Fitzsimmons and Jay Rosen", title = "{Markovian} loop soups: permanental processes and isomorphism theorems", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "60:1--60:30", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3255", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3255", abstract = "We construct loop soups for general Markov processes without transition densities and show that the associated permanental process is equal in distribution to the loop soup local time. This is used to establish isomorphism theorems connecting the local time of the original process with the associated permanental process. Further properties of the loop measure are studied.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "local times; loop soups; Markov processes; permanental processes", } @Article{DOvidio:2014:MFA, author = "Mirko D'Ovidio and Roberto Garra", title = "Multidimensional fractional advection-dispersion equations and related stochastic processes", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "61:1--61:31", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2854", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2854", abstract = "In this paper we study multidimensional fractional advection-dispersion equations involving fractional directional derivatives both from a deterministic and a stochastic point of view. For such equations we show the connection with a class of multidimensional L{\'e}vy processes. We introduce a novel L{\'e}vy-Khinchine formula involving fractional gradients and study the corresponding infinitesimal generator of multi-dimensional random processes. We also consider more general fractional transport equations involving Frobenius--Perron operators and their stochastic solutions. Finally, some results about fractional power of second order directional derivatives and their applications are also provided.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "directional derivatives; fractional advection equation; Fractional vector calculus", } @Article{Bi:2014:PMN, author = "Hongwei Bi and Jean-Fran{\c{c}}ois Delmas", title = "A population model with non-neutral mutations using branching processes with immigration", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "62:1--62:23", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2939", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2939", abstract = "We consider a stationary continuous model of random size population with non-neutral mutations using a continuous state branching process with non-homogeneous immigration. We assume the type (or mutation) of the immigrants is random given by a constant mutation rate measure. We determine some genealogical properties of this process such as: distribution of the time to the most recent common ancestor (MRCA), bottleneck effect at the time to the MRCA (which might be drastic for some mutation rate measures), favorable type for the MRCA, asymptotics of the number of ancestors.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bottleneck; branching process; genealogical tree; immigration; MRCA; non-neutral mutation; population model", } @Article{Garbit:2014:ETC, author = "Rodolphe Garbit and Kilian Raschel", title = "On the exit time from a cone for {Brownian} motion with drift", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "63:1--63:27", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3169", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3169", abstract = "We investigate the tail distribution of the first exit time of Brownian motion with drift from a cone and find its exact asymptotics for a large class of cones. Our results show in particular that its exponential decreasing rate is a function of the distance between the drift and the cone, whereas the polynomial part in the asymptotics depends on the position of the drift with respect to the cone and its polar cone, and reflects the local geometry of the cone at the points that minimize the distance to the drift.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Brownian motion with drift; Cone; Exit time; Heat kernel", } @Article{Kersting:2014:EBC, author = "G{\"o}tz Kersting and Jason Schweinsberg and Anton Wakolbinger", title = "The evolving beta coalescent", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "64:1--64:27", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3332", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3332", abstract = "In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time. As the population evolves over time, the tree that represents the genealogy of the population also changes, leading to a tree-valued stochastic process known as the evolving coalescent. Here we will consider the evolving coalescent for populations whose genealogy can be described by a beta coalescent, which is known to give the genealogy of populations with very large family sizes. We show that as the size of the population tends to infinity, the evolution of certain functionals of the beta coalescent, such as the total number of mergers, the total branch length, and the total length of external branches, converges to a stationary stable process. Our methods also lead to new proofs of known asymptotic results for certain functionals of the non-evolving beta coalescent.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "beta coalescent, evolving coalescent, total branch length, total external length, number of mergers, stable moving average processes", } @Article{Handa:2014:EPC, author = "Kenji Handa", title = "Ergodic properties for $ \alpha $-CIR models and a class of generalized {Fleming--Viot} processes", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "65:1--65:25", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2928", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2928", abstract = "We discuss a Markov jump process regarded as a variant of the CIR (Cox--Ingersoll--Ross) model and its infinite-dimensional extension. These models belong to a class of measure-valued branching processes with immigration, whose jump mechanisms are governed by certain stable laws. The main result gives a lower spectral gap estimate for the generator. As an application, a certain ergodic property is shown for the generalized Fleming--Viot process obtained as the time-changed ratio process.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "CIR model; generalized Fleming--Viot process; measure-valued branching process; spectral gap", } @Article{Bourguin:2014:PIP, author = "Solesne Bourguin and Giovanni Peccati", title = "Portmanteau inequalities on the {Poisson} space: mixed regimes and multidimensional clustering", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "66:1--66:42", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2879", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2879", abstract = "Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables. Several consequences are deduced from this result, in particular: (1) new abstract criteria for multidimensional stable convergence on the Poisson space, (2) a class of mixed limit theorems, involving both Poisson and Gaussian limits, (3) criteria for the asymptotic independence of U-statistics following Gaussian and Poisson asymptotic regimes. Our results generalize and unify several previous findings in the field. We provide an application to joint sub-graph counting in random geometric graphs.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Chen--Stein Method; Contractions; Malliavin Calculus; Poisson Limit Theorems; Poisson Space; Random Graphs; Total Variation Distance; Wiener Chaos", } @Article{Panchenko:2014:RSS, author = "Dmitry Panchenko", title = "On the replica symmetric solution of the {K-sat} model", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "67:1--67:17", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2963", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2963", abstract = "In this paper we translate Talagrand's solution of the K-sat model at high temperature into the language of asymptotic Gibbs measures. Using exact cavity equations in the infinite volume limit allows us to remove many technicalities of the inductions on the system size, which clarifies the main ideas of the proof. This approach also yields a larger region of parameters where the system is in a pure state and, in particular, for small connectivity parameter one can prove the replica symmetric formula for the free energy at any temperature.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "spin glasses, random K-sat model, replica symmetric solution", } @Article{Paulin:2014:CDI, author = "Daniel Paulin", title = "The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "68:1--68:34", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3261", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3261", abstract = "We prove concentration inequalities for general functions of weakly dependent random variables satisfying the Dobrushin condition. In particular, we show Talagrand's convex distance inequality for this type of dependence. We apply our bounds to a version of the stochastic salesman problem, the Steiner tree problem, the total magnetisation of the Curie--Weiss model with external field, and exponential random graph models. Our proof uses the exchangeable pair method for proving concentration inequalities introduced by Chatterjee (2005). Another key ingredient of the proof is a subclass of $ (a, b)$-self-bounding functions, introduced by Boucheron, Lugosi and Massart (2009).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "concentration inequalities; Dobrushin condition; exchangeable pairs; exponential random graph; reversible Markov chains; sampling without replacement; Stein's method; Steiner tree; stochastic travelling salesman problem", } @Article{Alm:2014:FCP, author = "Sven Erick Alm and Svante Janson and Svante Linusson", title = "First critical probability for a problem on random orientations in {$ G(n, p) $}", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "69:1--69:14", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2725", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2725", abstract = "We study the random graph $ G(n, p) $ with a random orientation. For three fixed vertices $ s, a, b $ in $ G(n, p) $ we study the correlation of the events $ \{ a \to s \} $ (there exists a directed path from $a$ to $s$) and $ \{ s \to b \} $. We prove that asymptotically the correlation is negative for small $p$, $ p < \frac {C_1}n$, where $ C_1 \approx 0.3617$, positive for $ \frac {C_1}n < p < \frac 2 n$ and up to $ p = p_2 (n)$. Computer aided computations suggest that $ p_2 (n) = \frac {C_2}n$, with $ C_2 \approx 7.5$. We conjecture that the correlation then stays negative for $p$ up to the previously known zero at $ \frac 12$; for larger $p$ it is positive.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Random directed graph, correlation, directed paths", } @Article{Pitman:2014:RTG, author = "Jim Pitman and Douglas Rizzolo and Matthias Winkel", title = "Regenerative tree growth: structural results and convergence", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "70:1--70:27", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3040", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3040", abstract = "We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n > =1, with a regenerative property at branch points. This framework includes growth processes for exchangeably labelled Markov branching trees, as well as non-exchangeable models such as the alpha-theta model, the alpha-gamma model and all restricted exchangeable models previously studied. Our main structural result is a representation of the growth rule by a sigma-finite dislocation measure kappa on the set of partitions of the natural numbers extending Bertoin's notion of exchangeable dislocation measures from the setting of homogeneous fragmentations. We use this representation to establish necessary and sufficient conditions on the growth rule under which we can apply results by Haas and Miermont for unlabelled and not necessarily consistent trees to establish self-similar random trees and residual mass processes as scaling limits. While previous studies exploited some form of exchangeability, our scaling limit results here only require a regularity condition on the convergence of asymptotic frequencies under kappa, in addition to a regular variation condition.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "regenerative composition, Markov branching model, fragmentation, self-similar tree, continuum random tree, R-tree, weighted R-tree, recursive random tree", } @Article{Heilman:2014:EPO, author = "Steven Heilman", title = "{Euclidean} partitions optimizing noise stability", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "71:1--71:37", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3083", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3083", abstract = "The Standard Simplex Conjecture of Isaksson and Mossel asks for the partition $ \{ A_i \}_{i = 1}^k $ of $ \mathbb {R}^n $ into $ k \leq n + 1 $ pieces of equal Gaussian measure of optimal noise stability. That is, for $ \rho > 0 $, we maximize\par $$ \sum_{i = 1}^k \int_{\mathbb {R}^n} \int_{\mathbb {R}^n}1_{A_i}(x)1_{A_i}(x \rho + y \sqrt {1 - \rho^2})e^{-(x_1^2 + \cdots + x_n^2) / 2}e^{-(y_1^2 + \cdots + y_n^2) / 2}d x d y. $$ Isaksson and Mossel guessed the best partition for this problem and proved some applications of their conjecture. For example, the Standard Simplex Conjecture implies the Plurality is Stablest Conjecture. For $ k = 3, n \geq 2 $ and $ 0 < \rho < \rho_0 (k, n) $, we prove the Standard Simplex Conjecture. The full conjecture has applications to theoretical computer science and to geometric multi-bubble problems (after Isaksson and Mossel).", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Standard simplex, plurality, optimization, MAX-k-CUT, Unique Games Conjecture", } @Article{Kuan:2014:GFF, author = "Jeffrey Kuan", title = "The {Gaussian} free field in interlacing particle systems", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "72:1--72:31", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3732", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3732", abstract = "We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the fluctuations of the height function converge to that of the Gaussian free field. In particular, this shows that a previously studied random surface growth model with a reflecting wall has Gaussian free field fluctuations.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Gaussian free field, determinantal point process, interlacing particles", } @Article{Dong:2014:MMD, author = "Zhao Dong and Xuhui Peng", title = "{Malliavin} matrix of degenerate {SDE} and gradient estimate", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "73:1--73:26", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3120", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3120", abstract = "In this article, we prove that the inverse of Malliavin matrix belongs to $ L^p(\Omega, \mathbb {P}) $ for a class of degenerate stochastic differential equation (SDE). The conditions required are similar to H{\"o}rmander's bracket condition, but we don't need all coefficients of the SDE are smooth. Furthermore, we obtain a locally uniform estimate for the Malliavin matrix and a gradient estimate. We also prove that the semigroup generated by the SDE is strong Feller. These results are illustrated through examples.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "H{\"o}rmander condition; Degenerate stochastic differential equation; Gradient estimate; Malliavin calculus; Strong Feller", } @Article{Bettinelli:2014:SLU, author = "J{\'e}r{\'e}mie Bettinelli and Emmanuel Jacob and Gr{\'e}gory Miermont", title = "The scaling limit of uniform random plane maps, via the {Ambj{\o}rn--Budd} bijection", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "74:1--74:16", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3213", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3213", abstract = "We prove that a uniform rooted plane map with n edges converges in distribution after asuitable normalization to the Brownian map for the Gromov--Hausdorff topology. A recent bijection due to Ambj{\o}rn and Budd allows to derive this result by a direct coupling with a uniform random quadrangulation with n faces.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "bijections; Brownian map; Gromov--Hausdorff topology; random maps; random metric spaces; scaling limits", } @Article{Evilsizor:2014:EGL, author = "Stephen Evilsizor and Nicolas Lanchier", title = "Evolutionary games on the lattice: best-response dynamics", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "75:1--75:12", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-3126", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3126", abstract = "The best-response dynamics is an example of an evolutionary game where players update their strategy in order to maximize their payoff. The main objective of this paper is to study a stochastic spatial version of this game based on the framework of interacting particle systems in which players are located on an infinite square lattice. In the presence of two strategies, and calling a strategy selfish or altruistic depending on a certain ordering of the coefficients of the underlying payoff matrix, a simple analysis of the nonspatial mean-field approximation of the spatial model shows that a strategy is evolutionary stable if and only if it is selfish, making the system bistable when both strategies are selfish. The spatial and nonspatial models agree when at least one strategy is altruistic. In contrast, we prove that in the presence of two selfish strategies and in any spatial dimension, only the most selfish strategy remains evolutionary stable. The main ingredients of the proof are monotonicity results and a coupling between the best-response dynamics properly rescaled in space with bootstrap percolation to compare the infinite time limits of both systems.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Interacting particle systems, evolutionary game, evolutionary stable strategy", } @Article{Torres:2014:QVF, author = "Soledad Torres and Ciprian Tudor and Frederi Viens", title = "Quadratic variations for the fractional-colored stochastic heat equation", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "76:1--76:51", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2698", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2698", abstract = "Using multiple stochastic integrals and Malliavin calculus, we analyze the quadratic variations of a class of Gaussian processes that contains the linear stochastic heat equation on $ \mathbf {R}^d $ driven by a non-white noise which is fractional Gaussian with respect to the time variable (Hurst parameter $H$) and has colored spatial covariance of $ \alpha $-Riesz-kernel type. The processes in this class are self-similar in time with a parameter $K$ distinct from $H$, and have path regularity properties which are very close to those of fractional Brownian motion (fBm) with Hurst parameter $K$ (in the heat equation case, $ K = H - (d - \alpha) / 4$ ). However the processes exhibit marked inhomogeneities which cause naive heuristic renormalization arguments based on $K$ to fail, and require delicate computations to establish the asymptotic behavior of the quadratic variation. A phase transition between normal and non-normal asymptotics appears, which does not correspond to the familiar threshold $ K = 3 / 4$ known in the case of fBm. We apply our results to construct an estimator for $H$ and to study its asymptotic behavior.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "fractional Brownian motion; Hurst parameter; Malliavin calculus; multiple stochastic integral; non-central limit theorem; quadratic variation; selfsimilarity; statistical estimation; stochastic heat equation", } @Article{Hayashi:2014:HCP, author = "Masafumi Hayashi and Arturo Kohatsu and Go Yuki", title = "{H{\"o}lder} continuity property of the densities of {SDEs} with singular drift coefficients", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "77:1--77:22", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2609", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2609", abstract = "We prove that the solution of stochastic differential equations with deterministic diffusion coefficient admits a H{\"o}lder continuous density via a condition on the integrability of the Fourier transform of the drift coefficient. In our result, the integrability is an important factor to determine the order of H{\"o}lder continuity of the density. Explicit examples and some applications are given.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Malliavin Calculus, non-smooth drift, density function, Fourier analysis", } @Article{Menz:2014:BLT, author = "Georg Menz", title = "A {Brascamp--Lieb} type covariance estimate", journal = j-ELECTRON-J-PROBAB, volume = "19", pages = "78:1--78:15", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v19-2997", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2997", abstract = "In this article, we derive a new covariance estimate. The estimate has a similar structure as the Brascamp--Lieb inequality and is optimal for ferromagnetic Gaussian measures. It can be naturally applied to deduce decay of correlations of lattice systems of continuous spins. We also discuss the relation of the new estimate with known estimates like a weighted estimate due to Helffer \& Ledoux. The main ingredient of the proof of the new estimate is a directional Poincar{\'e} inequality which seems to be unknown.", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "decay of correlations, Brascamp--Lieb, lattice systems, continuous spin", } @Article{Menard:2014:PUI, author = "Laurent M{\'e}nard and Pierre Nolin", title = "Percolation on uniform infinite planar maps", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "79:1--79:27", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2675", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Boutillier:2014:HRX, author = "C{\'e}dric Boutillier and B{\'e}atrice de Tili{\`e}re", title = "Height representation of {XOR--Ising} loops via bipartite dimers", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "80:1--80:33", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2449", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hasebe:2014:FID, author = "Takahiro Hasebe", title = "Free infinite divisibility for beta distributions and related ones", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "81:1--81:33", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3448", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ercolani:2014:RPS, author = "Nicholas M. Ercolani and Sabine Jansen and Daniel Ueltschi", title = "Random partitions in statistical mechanics", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "82:1--82:37", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3244", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Darling:2014:RDS, author = "Richard W. R. Darling and Mathew D. Penrose and Andrew R. Wade and Sandy L. Zabell", title = "Rank deficiency in sparse random {$ {\rm GF}[2][2] $} matrices", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "83:1--83:36", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2458", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Wang:2014:SAD, author = "Ruodu Wang", title = "Sum of arbitrarily dependent random variables", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "84:1--84:18", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3373", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Dobbs:2014:SDT, author = "Daniel Dobbs and Tai Melcher", title = "Small deviations for time-changed {Brownian} motions and applications to second-order chaos", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "85:1--85:23", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2993", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Zhang:2014:GPA, author = "Lixin Zhang", title = "A {Gaussian} process approximation for two-color randomly reinforced urns", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "86:1--86:19", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3432", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Dehling:2014:SEC, author = "Herold Dehling and Olivier Durieu and Marco Tusche", title = "A sequential empirical {CLT} for multiple mixing processes with application to {$ B \mathcal {B} $}-geometrically ergodic {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "87:1--87:26", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3216", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Denisov:2014:LPR, author = "Denis Denisov and Vladimir Vatutin and Vitali Wachtel", title = "Local probabilities for random walks with negative drift conditioned to stay nonnegative", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "88:1--88:17", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3426", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Flores:2014:FED, author = "Gregorio R. Moreno Flores and Timo Sepp{\"a}l{\"a}inen and Benedek Valk{\'o}", title = "Fluctuation exponents for directed polymers in the intermediate disorder regime", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "89:1--89:28", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3307", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Acosta:2014:TRM, author = "Javier Acosta", title = "Tightness of the recentered maximum of log-correlated {Gaussian} fields", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "90:1--90:25", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3170", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chen:2014:SCC, author = "Xin Chen and Xue-Mei Li", title = "Strong completeness for a class of stochastic differential equations with irregular coefficients", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "91:1--91:34", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3293", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hillion:2014:IPM, author = "Erwan Hillion", title = "{$ W_{1, +} $}-interpolation of probability measures on graphs", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "92:1--92:29", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3336", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Gouezel:2014:MBC, author = "S{\'e}bastien Gou{\"e}zel and Ian Melbourne", title = "Moment bounds and concentration inequalities for slowly mixing dynamical systems", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "93:1--93:30", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3427", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Berard:2014:LCL, author = "Jean B{\'e}rard and Pierre {Del Moral} and Arnaud Doucet", title = "A lognormal central limit theorem for particle approximations of normalizing constants", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "94:1--94:28", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3428", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Beiglbock:2014:MID, author = "Mathias Beiglb{\"o}ck and Marcel Nutz", title = "Martingale inequalities and deterministic counterparts", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "95:1--95:15", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3270", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Rhodes:2014:HKD, author = "R{\'e}mi Rhodes and Christophe Garban and Vincent Vargas", title = "On the heat kernel and the {Dirichlet} form of {Liouville} {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "96:1--96:25", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2950", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kliem:2014:CCR, author = "Sandra Kliem", title = "A compact containment result for nonlinear historical superprocess approximations for population models with trait-dependence", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "97:1--97:13", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3506", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Lin:2014:HMB, author = "Shen Lin", title = "The harmonic measure of balls in critical {Galton--Watson} trees with infinite variance offspring distribution", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "98:1--98:35", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3498", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Nourdin:2014:ITF, author = "Ivan Nourdin and Raghid Zeineddine", title = "An {It{\^o}} type formula for the fractional {Brownian} motion in {Brownian} time", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "99:1--99:15", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3184", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hansen:2014:CIS, author = "Niels Richard Hansen and Alexander Sokol", title = "Causal interpretation of stochastic differential equations", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "100:1--100:24", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2891", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Balanca:2014:FRL, author = "Paul Balan{\c{c}}a", title = "Fine regularity of {L{\'e}vy} processes and linear (multi)fractional stable motion", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "101:1--101:37", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3393", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Eichelsbacher:2014:NBE, author = "Peter Eichelsbacher and Christoph Th{\"a}le", title = "New {Berry--Ess{\'e}en} bounds for non-linear functionals of {Poisson} random measures", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "102:1--102:25", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3061", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Qinwen:2014:JCS, author = "Wang Qinwen and Su Zhonggen and Yao Jianfeng", title = "Joint {CLT} for several random sesquilinear forms with applications to large-dimensional spiked population models", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "103:1--103:28", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3339", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Huang:2014:CER, author = "Chunmao Huang and Quansheng Liu", title = "Convergence in {$ L^p $} and its exponential rate for a branching process in a random environment", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "104:1--104:22", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3388", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Dick:2014:DEV, author = "Josef Dick and Daniel Rudolf", title = "Discrepancy estimates for variance bounding {Markov} chain quasi-{Monte Carlo}", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "105:1--105:24", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3132", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Dembo:2014:WWG, author = "Amir Dembo and Ruojun Huang and Vladas Sidoravicius", title = "Walking within growing domains: recurrence versus transience", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "106:1--106:20", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3272", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Menz:2014:AOR, author = "Georg Menz", title = "The approach of {Otto--Reznikoff} revisited", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "107:1--107:27", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3418", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Curien:2014:RSL, author = "Nicolas Curien and Igor Kortchemski", title = "Random stable looptrees", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "108:1--108:35", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2732", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Damron:2014:SCF, author = "Michael Damron and Jack Hanson and Philippe Sosoe", title = "Subdiffusive concentration in first passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "109:1--109:27", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3680", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bally:2014:DBP, author = "Vlad Bally and Lucia Caramellino", title = "On the distances between probability density functions", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "110:1--110:33", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3175", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Heydenreich:2014:SBR, author = "Markus Heydenreich and Franz Merkl and Silke W. W. Rolles", title = "Spontaneous breaking of rotational symmetry in the presence of defects", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "111:1--111:17", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2971", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Khandwawala:2014:BPM, author = "Mustafa Khandwawala", title = "Belief propagation for minimum weight many-to-one matchings in the random complete graph", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "112:1--112:40", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3491", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chen:2014:TPR, author = "Jun Chen", title = "Two particles' repelling random walks on the complete graph", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "113:1--113:17", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2669", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Allez:2014:SKP, author = "Romain Allez and Laure Dumaz", title = "From sine kernel to {Poisson} statistics", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "114:1--114:25", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3742", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Baumdicker:2014:IMG, author = "Franz Baumdicker and Peter Pfaffelhuber", title = "The infinitely many genes model with horizontal gene transfer", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "115:1--115:27", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2642", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Rios-Zertuche:2014:PDN, author = "Rodolfo Rios-Zertuche", title = "The pillowcase distribution and near-involutions", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "116:1--116:22", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3626", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Gamlin:2014:ABB, author = "Samuel L. Gamlin and Antal A. J{\'a}rai", title = "Anchored burning bijections on finite and infinite graphs", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "117:1--117:23", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3542", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Slominski:2014:WZT, author = "Leszek Slominski", title = "On {Wong--Zakai} type approximations of reflected diffusions", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "118:1--118:15", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3425", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Graczyk:2014:SSN, author = "Piotr Graczyk and Jacek Ma{\l}ecki", title = "Strong solutions of non-colliding particle systems", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "119:1--119:21", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3842", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hsiau:2014:LRF, author = "Shoou-Ren Hsiau and Yi-Shen Lin and Yi-Ching Yao", title = "Logconcave reward functions and optimal stopping rules of threshold form", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "120:1--120:18", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3745", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Durrett:2014:SEG, author = "Rick Durrett", title = "Spatial evolutionary games with small selection coefficients", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "121:1--121:64", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3621", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Beghin:2014:FPP, author = "Luisa Beghin and Mirko D'Ovidio", title = "Fractional {Poisson} process with random drift", journal = j-ELECTRON-J-PROBAB, volume = "19", number = "??", pages = "122:1--122:26", month = "????", year = "2014", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:18 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/19; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3258", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Fan:2015:EIM, author = "Xiequan Fan and Ion Grama and Quansheng Liu", title = "Exponential inequalities for martingales with applications", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "1:1--1:22", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3496", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chang:2015:LCD, author = "Yinshan Chang", title = "Loop cluster on discrete circles", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "2:1--2:32", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3176", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Mountford:2015:RWG, author = "Thomas S. Mountford and Maria Eulalia Vares", title = "Random walks generated by equilibrium contact processes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "3:1--3:17", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3439", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Holmgren:2015:LLF, author = "Cecilia Holmgren and Svante Janson", title = "Limit laws for functions of fringe trees for binary search trees and random recursive trees", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "4:1--4:51", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3627", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ayyer:2015:MJP, author = "Arvind Ayyer and J{\'e}r{\'e}mie Bouttier and Sylvie Corteel and Fran{\c{c}}ois Nunzi", title = "Multivariate juggling probabilities", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "5:1--5:29", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3495", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Alexander:2015:DPR, author = "Kenneth S. Alexander and G{\"o}khan Y{\i}ld{\i}r{\i}m", title = "Directed polymers in a random environment with a defect line", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "6:1--6:20", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3379", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Rebeschini:2015:PTN, author = "Patrick Rebeschini and Ramon van Handel", title = "Phase transitions in nonlinear filtering", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "7:1--7:46", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3281", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Caputo:2015:MLP, author = "Pietro Caputo and Fabio Martinelli and Fabio Lucio Toninelli", title = "Multi-level pinning problems for random walks and self-avoiding lattice paths", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "8:1--8:29", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3849", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Holmgren:2015:ADT, author = "Cecilia Ingrid Holmgren and Svante Janson", title = "Asymptotic distribution of two-protected nodes in ternary search trees", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "9:1--9:20", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Feb 10 12:30:22 MST 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3577", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Field:2015:EPT, author = "Laurence S. Field and Gregory F. Lawler", title = "Escape probability and transience for {SLE}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "10:1--10:14", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3714", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Travers:2015:ILI, author = "Nicholas Travers", title = "Inversions and longest increasing subsequence for $k$-card-minimum random permutations", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "11:1--11:27", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3602", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Diomande:2015:MPO, author = "Bakarime Diomande and Adrian Zalinescu", title = "Maximum principle for an optimal control problem associated to a stochastic variational inequality with delay", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "12:1--12:35", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2741", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Burdzy:2015:STG, author = "Krzysztof Burdzy", title = "Stirring two grains of sand", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "13:1--13:29", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3845", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Merlevede:2015:SAA, author = "Florence Merlev{\`e}de and Emmanuel Rio", title = "Strong approximation for additive functionals of geometrically ergodic {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "14:1--14:27", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3746", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Spiliopoulos:2015:QLD, author = "Konstantinos Spiliopoulos", title = "Quenched large deviations for multiscale diffusion processes in random environments", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "15:1--15:29", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3729", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Goldschmidt:2015:LBC, author = "Christina Goldschmidt and B{\'e}n{\'e}dicte Haas", title = "A line-breaking construction of the stable trees", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "16:1--16:24", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3690", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Lacoin:2015:MPM, author = "Hubert Lacoin and Augusto Teixeira", title = "A mathematical perspective on metastable wetting", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "17:1--17:23", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3241", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Louidor:2015:LDE, author = "Oren Louidor and Will Perkins", title = "Large deviations for the empirical distribution in the branching random walk", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "18:1--18:19", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2147", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Levajkovic:2015:SEE, author = "Tijana Levajkovi{\'c} and Stevan Pilipovi{\'c} and Dora Sele{\v{s}}i and Milica {\v{Z}}igi{\'c}", title = "Stochastic evolution equations with multiplicative noise", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "19:1--19:23", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3696", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Deligiannidis:2015:AVS, author = "George Deligiannidis and Magda Peligrad and Sergey Utev", title = "Asymptotic variance of stationary reversible and normal {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "20:1--20:26", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3183", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Song:2015:RDS, author = "Yulin Song and Xicheng Zhang", title = "Regularity of density for {SDEs} driven by degenerate {L{\'e}vy} noises", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "21:1--21:27", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3287", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Buraczewski:2015:RCK, author = "Dariusz Buraczewski and Ewa Damek and Tomasz Przebinda", title = "On the rate of convergence in the {Kesten} renewal theorem", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "22:1--22:35", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3708", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Alishahi:2015:SEU, author = "Kasra Alishahi and Mohammadsadegh Zamani", title = "The spherical ensemble and uniform distribution of points on the sphere", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "23:1--23:27", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3733", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Guerra:2015:AED, author = "Enrique Guerra and Alejandro F. Ramirez", title = "Almost exponential decay for the exit probability from slabs of ballistic {RWRE}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "24:1--24:17", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3655", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{OConnell:2015:TWA, author = "Neil O'Connell and Janosch Ortmann", title = "{Tracy--Widom} asymptotics for a random polymer model with gamma-distributed weights", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "25:1--25:18", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3787", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Can:2015:MCP, author = "Van Hao Can and Bruno Schapira", title = "Metastability for the contact process on the configuration model with infinite mean degree", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "26:1--26:22", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3859", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Demichel:2015:DEC, author = "Yann Demichel and Ana-Karina Fermin and Philippe Soulier", title = "The diameter of an elliptical cloud", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "27:1--27:32", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3777", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Roberts:2015:FAC, author = "Matthew Iain Roberts", title = "Fine asymptotics for the consistent maximal displacement of branching {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "28:1--28:26", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2912", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Sarantsev:2015:TSC, author = "Andrey Sarantsev", title = "Triple and simultaneous collisions of competing {Brownian} particles", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "29:1--29:28", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3279", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Villemonais:2015:MQS, author = "Denis Villemonais", title = "Minimal quasi-stationary distribution approximation for a birth and death process", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "30:1--30:18", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3482", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Valle:2015:SLR, author = "Glauco Valle and Luiz Renato Fontes and Leon Alexander Valencia", title = "Scaling limit of the radial {Poissonian} web", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "31:1--31:40", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3395", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Andjel:2015:SCP, author = "Enrique Andjel and Fran{\c{c}}ois Ezanno and Pablo Groisman and Leonardo T. Rolla", title = "Subcritical contact process seen from the edge: Convergence to quasi-equilibrium", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "32:1--32:16", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3881", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Rousselle:2015:QIP, author = "Arnaud Rousselle", title = "Quenched invariance principle for random walks on {Delaunay} triangulations", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "33:1--33:32", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4006", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Berti:2015:TVF, author = "Patrizia Berti and Luca Pratelli and Pietro Rigo", title = "Two versions of the fundamental theorem of asset pricing", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "34:1--34:21", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3321", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Aldous:2015:CGP, author = "David Aldous and Daniel Lanoue and Justin Salez", title = "The compulsive gambler process", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "35:1--35:18", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3582", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Latala:2015:NSC, author = "Rafa{\l} Lata{\l}a and Tomasz Tkocz", title = "A note on suprema of canonical processes based on random variables with regular moments", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "36:1--36:17", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3625", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Grubel:2015:RRT, author = "Rudolf Gr{\"u}bel and Igor Michailow", title = "Random recursive trees: a boundary theory approach", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "37:1--37:22", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3832", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Jacka:2015:CTR, author = "Saul Jacka and Aleksandar Mijatovic", title = "Coupling and tracking of regime-switching martingales", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "38:1--38:39", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2307", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chouk:2015:SSI, author = "Khalil Chouk and Samy Tindel", title = "{Skorohod} and {Stratonovich} integration in the plane", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "39:1--39:39", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3041", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Favaro:2015:LDP, author = "Stefano Favaro and Shui Feng", title = "Large deviation principles for the {Ewens--Pitman} sampling model", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "40:1--40:26", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3668", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Broman:2015:PCH, author = "Erik Ivar Broman and Johan Tykesson", title = "{Poisson} cylinders in hyperbolic space", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "41:1--41:25", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3645", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Adamczak:2015:COU, author = "Rados{\l}aw Adamczak and Piotr Mi{\l}o{\'s}", title = "{CLT} for {Ornstein--Uhlenbeck} branching particle system", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "42:1--42:35", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4233", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Berzunza:2015:YPR, author = "Gabriel Berzunza", title = "{Yule} processes with rare mutation and their applications to percolation on $b$-ary trees", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "43:1--43:23", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3789", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Matic:2015:EDW, author = "Ivan Matic and David Sivakoff", title = "Excited deterministic walk in a random environment", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "44:1--44:19", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3874", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Limic:2015:DLS, author = "Vlada Limic and Anna Talarczyk", title = "Diffusion limits at small times for {$ \Lambda $}-coalescents with a {Kingman} component", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "45:1--45:20", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3818", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Perkowski:2015:LTT, author = "Nicolas Perkowski and David J. Pr{\"o}mel", title = "Local times for typical price paths and pathwise {Tanaka} formulas", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "46:1--46:15", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3534", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Drewitz:2015:HDA, author = "Alexander Drewitz and Pierre-Fran{\c{c}}ois Rodriguez", title = "High-dimensional asymptotics for percolation of {Gaussian} free field level sets", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "47:1--47:39", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3416", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Juszczyszyn:2015:HTP, author = "Tomasz Juszczyszyn and Mateusz Kwa{\'s}nicki", title = "Hitting times of points for symmetric {L{\'e}vy} processes with completely monotone jumps", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "48:1--48:24", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3440", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Mountford:2015:LER, author = "Thomas Mountford and Jean-Christophe Mourrat", title = "{Lyapunov} exponents of random walks in small random potential: the upper bound", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "49:1--49:18", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3489", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Turkedjiev:2015:TAD, author = "Plamen Turkedjiev", title = "Two algorithms for the discrete time approximation of {Markovian} backward stochastic differential equations under local conditions", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "50:1--50:49", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3022", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Lupu:2015:VTB, author = "Titus Lupu and Jim Pitman and Wenpin Tang", title = "The {Vervaat} transform of {Brownian} bridges and {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "51:1--51:31", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3744", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kolesko:2015:FPM, author = "Konrad Kolesko and Sebastian Mentemeier", title = "Fixed points of the multivariate smoothing transform: the critical case", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "52:1--52:24", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4022", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Dirksen:2015:TBG, author = "Sjoerd Dirksen", title = "Tail bounds via generic chaining", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "53:1--53:29", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3760", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Balan:2015:SAM, author = "Raluca M. Balan and Maria Jolis and Lluis Quer-Sardanyons", title = "{SPDEs} with affine multiplicative fractional noise in space with index {$ \frac {1}{4} < H < \frac {1}{2} $}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "54:1--54:36", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3719", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hu:2015:SHE, author = "Yaozhong Hu and Jingyu Huang and David Nualart and Samy Tindel", title = "Stochastic heat equations with general multiplicative {Gaussian} noises: {H{\"o}lder} continuity and intermittency", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "55:1--55:50", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3316", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Andreoletti:2015:LNV, author = "Pierre Andreoletti and Alexis Devulder", title = "Localization and number of visited valleys for a transient diffusion in random environment", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "56:1--56:58", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3173", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Lecue:2015:MRC, author = "Guillaume Lecu{\'e} and Shahar Mendelson", title = "Minimax rate of convergence and the performance of empirical risk minimization in phase recovery", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "57:1--57:29", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3525", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Fearnhead:2015:TDC, author = "Paul Fearnhead and Paul Jenkins and Yun Song", title = "Tractable diffusion and coalescent processes for weakly correlated loci", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "58:1--58:25", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3564", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Arguin:2015:PDS, author = "Louis-Pierre Arguin and Olivier Zindy", title = "{Poisson--Dirichlet} Statistics for the extremes of the two-dimensional discrete {Gaussian} free field", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "59:1--59:19", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3077", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Larsson:2015:MVB, author = "Martin Larsson", title = "Matrix-valued {Bessel} processes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "60:1--60:29", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3785", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Pitman:2015:SZS, author = "Jim Pitman and Wenpin Tang", title = "The {Slepian} zero set, and {Brownian} bridge embedded in {Brownian} motion by a spacetime shift", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "61:1--61:28", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3911", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hu:2015:MVS, author = "Yueyun Hu and Zhan Shi", title = "The most visited sites of biased random walks on trees", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "62:1--62:14", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4051", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Shao:2015:CTR, author = "Jinghai Shao", title = "Criteria for transience and recurrence of regime-switching diffusion processes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "63:1--63:15", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4018", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Lanoue:2015:IM, author = "Daniel Parmet Lanoue", title = "The {iPod} Model", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "64:1--64:20", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3559", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kazi-Tani:2015:SOB, author = "Nabil Kazi-Tani and Dylan Possama{\"\i} and Chao Zhou", title = "Second order {BSDEs} with jumps: existence and probabilistic representation for fully-nonlinear {PIDEs}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "65:1--65:31", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3569", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Possamai:2015:QBJ, author = "Dylan Possamai and Nabil Kazi-Tani and Chao Zhou", title = "Quadratic {BSDEs} with jumps: a fixed-point approach", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "66:1--66:28", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3363", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Costantini:2015:VMG, author = "Cristina Costantini and Thomas Gordon Kurtz", title = "Viscosity methods giving uniqueness for martingale problems", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "67:1--67:27", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3624", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Mallein:2015:MDB, author = "Bastien Mallein", title = "Maximal displacement in a branching random walk through interfaces", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "68:1--68:40", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2828", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ferrari:2015:BMO, author = "Patrik Lino Ferrari and Herbert Spohn and Thomas Weiss", title = "{Brownian} motions with one-sided collisions: the stationary case", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "69:1--69:41", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4177", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Alfonsi:2015:OTB, author = "Aur{\'e}lien Alfonsi and Benjamin Jourdain and Arturo Kohatsu-Higa", title = "Optimal transport bounds between the time-marginals of a multidimensional diffusion and its {Euler} scheme", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "70:1--70:31", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4195", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Berger:2015:CCP, author = "Quentin Berger and Julien Poisat", title = "On the critical curves of the pinning and copolymer models in correlated {Gaussian} environment", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "71:1--71:35", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3514", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Pham:2015:MRS, author = "Cong Dan Pham", title = "Monotonicity and regularity of the speed for excited random walks in higher dimensions", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "72:1--72:25", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3522", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kliem:2015:EMF, author = "Sandra Kliem and Wolfgang Loehr", title = "Existence of mark functions in marked metric measure spaces", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "73:1--73:24", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3969", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Murugan:2015:ATB, author = "Mathav Kishore Murugan and Laurent Saloff-Coste", title = "Anomalous threshold behavior of long range random walks", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "74:1--74:21", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3989", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bansaye:2015:SLG, author = "Vincent Bansaye and Florian Simatos", title = "On the scaling limits of {Galton--Watson} processes in varying environments", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "75:1--75:36", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3812", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chen:2015:CCT, author = "Guan-Yu Chen and Laurent Saloff-Coste", title = "Computing cutoff times of birth and death chains", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "76:1--76:47", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4077", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Towsner:2015:LSM, author = "Henry Piers Towsner", title = "Limits of sequences of {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "77:1--77:23", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4188", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Huckemann:2015:SCL, author = "Stephan Huckemann and Jonathan Mattingly and Ezra Miller and James Nolen", title = "Sticky central limit theorems at isolated hyperbolic planar singularities", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "78:1--78:34", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3887", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Paulin:2015:CIM, author = "Daniel Paulin", title = "Concentration inequalities for {Markov} chains by {Marton} couplings and spectral methods", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "79:1--79:32", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4039", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Budhiraja:2015:LRE, author = "Amarjit Budhiraja and Paul Dupuis and Markus Fischer and Kavita Ramanan", title = "Limits of relative entropies associated with weakly interacting particle systems", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "80:1--80:22", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4003", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Budhiraja:2015:LSK, author = "Amarjit Budhiraja and Paul Dupuis and Markus Fischer and Kavita Ramanan", title = "Local stability of {Kolmogorov} forward equations for finite state nonlinear {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "81:1--81:30", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4004", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Trutnau:2015:CSB, author = "Gerald Trutnau and Youssef Ouknine and Francesco Russo", title = "On countably skewed {Brownian} motion with accumulation point", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "82:1--82:27", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3640", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hobson:2015:ISS, author = "David Hobson", title = "Integrability of solutions of the {Skorokhod} embedding problem for diffusions", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "83:1--83:26", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4121", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Balazs:2015:DDB, author = "Marton Balazs and Attila Laszlo Nagy", title = "Dependent double branching annihilating random walk", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "84:1--84:32", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4045", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Jiao:2015:GDA, author = "Ying Jiao and Shanqiu Li", title = "Generalized density approach in progressive enlargement of filtrations", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "85:1--85:21", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3296", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Wieczorek:2015:SPM, author = "Rados{\l}aw Wieczorek", title = "A stochastic particles model of fragmentation process with shattering", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "86:1--86:17", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4060", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Spohn:2015:PIB, author = "Herbert Spohn and Tomohiro Sasamoto", title = "Point-interacting {Brownian} motions in the {KPZ} universality class", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "87:1--87:28", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3926", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Maller:2015:SLZ, author = "Ross A. Maller", title = "Strong laws at zero for trimmed {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "88:1--88:24", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3839", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bassetti:2015:IES, author = "Federico Bassetti and Lucia Ladelli and Daniel Matthes", title = "Infinite energy solutions to inelastic homogeneous {Boltzmann} equations", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "89:1--89:34", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3531", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Assaf:2015:QTS, author = "Sami Assaf and Noah Mills Forman and Jim Pitman", title = "The quantile transform of simple walks and {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "90:1--90:39", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3479", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Doney:2015:ABF, author = "Ronald Arthur Doney and Victor Rivero", title = "Asymptotic behaviour of first passage time distributions for subordinators", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "91:1--91:28", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3879", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Delarue:2015:LEM, author = "Fran{\c{c}}ois Delarue and St{\'e}phane Menozzi and Eulalia Nualart", title = "The {Landau} equation for {Maxwellian} molecules and the {Brownian} motion on {$ {\rm SO}_R(N) $}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "92:1--92:39", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4012", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bao:2015:HFS, author = "Jianhai Bao and Feng-Yu Wang and Chenggui Yuan", title = "Hypercontractivity for functional stochastic partial differential equations", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "93:1--93:15", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4108", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Depperschmidt:2015:MTV, author = "Andrej Depperschmidt and {\'E}tienne Pardoux and Peter Pfaffelhuber", title = "A mixing tree-valued process arising under neutral evolution with recombination", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "94:1--94:22", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4286", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hilario:2015:RWR, author = "Marcelo Hil{\'a}rio and Frank den Hollander and Vladas Sidoravicius and Renato Soares dos Santos and Augusto Teixeira", title = "Random walk on random walks", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "95:1--95:35", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4437", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ceci:2015:LRM, author = "Claudia Ceci and Alessandra Cretarola and Katia Colaneri", title = "Local risk-minimization under restricted information on asset prices", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "96:1--96:30", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3204", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Junge:2015:CIE, author = "Matthew Junge", title = "Choices, intervals and equidistribution", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "97:1--97:18", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4191", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Baur:2015:FPI, author = "Erich Baur and Jean Bertoin", title = "The fragmentation process of an infinite recursive tree and {Ornstein--Uhlenbeck} type processes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "98:1--98:20", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3866", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Benjamini:2015:FPP, author = "Itai Benjamini and Romain Tessera", title = "First passage percolation on nilpotent {Cayley} graphs and beyond", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "99:1--99:20", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3940", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Eon:2015:GAN, author = "Richard Eon and Mihai Gradinaru", title = "{Gaussian} asymptotics for a non-linear {Langevin} type equation driven by an $ \alpha $-stable {L{\'e}vy} noise", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "100:1--100:19", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4068", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Crane:2015:CGD, author = "Edward Crane and Nic Freeman and B{\'a}lint T{\'o}th", title = "Cluster growth in the dynamical {Erd{\H{o}}s--R{\'e}nyi} process with forest fires", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "101:1--101:33", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Sep 24 12:07:31 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4035", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Veto:2015:TWL, author = "B{\'a}lint Vet{\H{o}}", title = "{Tracy--Widom} limit of $q$-{Hahn} {TASEP}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "102:1--102:22", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4241", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Tarrago:2015:AIL, author = "Pierre Tarrago", title = "Asymptotic independence in large random permutations with fixed descent set", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "103:1--103:33", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4196", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Webb:2015:CPR, author = "Christian Webb", title = "The characteristic polynomial of a random unitary matrix and {Gaussian} multiplicative chaos --- The {$ L^2 $}-phase", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "104:1--104:21", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4296", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Huveneers:2015:RWD, author = "Fran{\c{c}}ois Huveneers and Fran{\c{c}}ois Simenhaus", title = "Random walk driven by simple exclusion process", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "105:1--105:42", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3906", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Lamacz:2015:MBC, author = "Agnes Lamacz and Stefan Neukamm and Felix Otto", title = "Moment bounds for the corrector in stochastic homogenization of a percolation model", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "106:1--106:30", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3618", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bhamidi:2015:IST, author = "Shankar Bhamidi and Jan Hannig and Chia Ying Lee and James Nolen", title = "The importance sampling technique for understanding rare events in {Erd{\H{o}}s--R{\'e}nyi} random graphs", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "107:1--107:30", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/2696", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chhaibi:2015:BGA, author = "Reda Chhaibi", title = "Beta-gamma algebra identities and {Lie}-theoretic exponential functionals of {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "108:1--108:20", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3666", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Dobler:2015:SME, author = "Christian D{\"o}bler", title = "{Stein}'s method of exchangeable pairs for the Beta distribution and generalizations", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "109:1--109:34", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3933", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Angst:2015:KBM, author = "J{\"u}rgen Angst and Isma{\"e}l Bailleul and Camille Tardif", title = "Kinetic {Brownian} motion on {Riemannian} manifolds", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "110:1--110:40", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4054", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Herzog:2015:NISa, author = "David P. Herzog and Jonathan C. Mattingly", title = "Noise-induced stabilization of planar flows {I}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "111:1--111:43", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4047", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Chiarini:2015:LCL, author = "Alberto Chiarini and Jean-Dominique Deuschel", title = "Local central limit theorem for diffusions in a degenerate and unbounded random medium", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "112:1--112:30", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4190", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Herzog:2015:NISb, author = "David P. Herzog and Jonathan C. Mattingly", title = "Noise-induced stabilization of planar flows {II}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "113:1--113:37", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4048", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Wintenberger:2015:WTI, author = "Olivier Wintenberger", title = "Weak transport inequalities and applications to exponential and oracle inequalities", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "114:1--114:27", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3558", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hulshof:2015:OAE, author = "Tim Hulshof", title = "The one-arm exponent for mean-field long-range percolation", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "115:1--115:26", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3935", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Baroni:2015:FSC, author = "Enrico Baroni and Remco van der Hofstad and Julia Komjathy", title = "Fixed speed competition on the configuration model with infinite variance degrees: unequal speeds", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "116:1--116:48", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3749", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Drewitz:2015:ALP, author = "Alexander Drewitz and Michael Scheutzow and Maite Wilke-Berenguer", title = "Asymptotics for {Lipschitz} percolation above tilted planes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "117:1--117:23", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4251", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Lalley:2015:CBB, author = "Steven P. Lalley and Bowei Zheng", title = "Critical branching {Brownian} motion with killing", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "118:1--118:29", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4466", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Zanella:2015:BSP, author = "Giacomo Zanella and Sergei Zuyev", title = "Branching-stable point processes", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "119:1--119:26", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4158", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Venker:2015:ESU, author = "Martin Venker and Kristina Schubert", title = "Empirical spacings of unfolded eigenvalues", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "120:1--120:37", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4436", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Kargin:2015:LTL, author = "Vladislav Kargin", title = "Limit theorems for linear eigenvalue statistics of overlapping matrices", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "121:1--121:30", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3937", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Fernandez:2015:AEH, author = "Roberto Fernandez and Francesco Manzo and Francesca Romana Nardi and Elisabetta Scoppola", title = "Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "122:1--122:37", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3656", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Eichelsbacher:2015:MSM, author = "Peter Eichelsbacher and Christoph Th{\"a}le", title = "{Malliavin--Stein} method for variance-gamma approximation on {Wiener} space", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "123:1--123:28", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4136", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Ding:2015:PAS, author = "Jian Ding and Subhajit Goswami", title = "Percolation of averages in the stochastic mean field model: the near-supercritical regime", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "124:1--124:21", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4111", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Dereudre:2015:IVC, author = "David Dereudre and Pierre Houdebert", title = "Infinite volume continuum random cluster model", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "125:1--125:24", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4718", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Storm:2015:OLR, author = "Julia Storm and Dirk Zeindler", title = "The order of large random permutations with cycle weights", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "126:1--126:34", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4331", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Fromm:2015:FAS, author = "Alexander Fromm and Peter Imkeller and David J. Pr{\"o}mel", title = "An {FBSDE} approach to the {Skorokhod} embedding problem for {Gaussian} processes with non-linear drift", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "127:1--127:38", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3758", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Monmarche:2015:ECC, author = "Pierre Monmarch{\'e}", title = "On {$ \mathcal {H}^1 $} and entropic convergence for contractive {PDMP}", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "128:1--128:30", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3581", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Richier:2015:UAC, author = "Lo{\"\i}c Richier", title = "Universal aspects of critical percolation on random half-planar maps", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "129:1--129:45", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sun Jan 10 11:11:03 MST 2016", bibsource = "http://ejp.ejpecp.org/index.php/ejp/issue/view/20; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/4041", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Hachem:2016:LCC, author = "Walid Hachem and Adrien Hardy and Jamal Najim", title = "Large complex correlated {Wishart} matrices: the {Pearcey} kernel and expansion at the hard edge", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "1:1--1:36", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454514661", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gubinelli:2016:FAA, author = "Massimiliano Gubinelli and Peter Imkeller and Nicolas Perkowski", title = "A {Fourier} analytic approach to pathwise stochastic integration", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "2:1--2:37", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454514662", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dereich:2016:PAF, author = "Steffen Dereich", title = "Preferential attachment with fitness: unfolding the condensate", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "3:1--3:38", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454514663", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ahlberg:2016:IFP, author = "Daniel Ahlberg and Michael Damron and Vladas Sidoravicius", title = "Inhomogeneous first-passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "4:1--4:19", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454514664", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chelkak:2016:CPT, author = "Dmitry Chelkak and Hugo Duminil-Copin and Cl{\'e}ment Hongler", title = "Crossing probabilities in topological rectangles for the critical planar {FK-Ising} model", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "5:1--5:28", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454682886", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bachmann:2016:CBG, author = "Sascha Bachmann and Giovanni Peccati", title = "Concentration bounds for geometric {Poisson} functionals: Logarithmic {Sobolev} inequalities revisited", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "6:1--6:44", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454682887", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Busani:2016:AUC, author = "Ofer Busani", title = "Aging uncoupled continuous time random walk limits", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "7:1--7:17", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454682888", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gilch:2016:AER, author = "Lorenz A. Gilch", title = "Asymptotic entropy of random walks on regular languages over a finite alphabet", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "8:1--8:42", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454682889", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bhatnagar:2016:DCH, author = "Nayantara Bhatnagar and Allan Sly and Prasad Tetali", title = "Decay of correlations for the hardcore model on the $d$-regular random graph", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "9:1--9:42", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1454682890", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Geiss:2016:MDR, author = "Christel Geiss and Alexander Steinicke", title = "{Malliavin} derivative of random functions and applications to {L{\'e}vy} driven {BSDEs}", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "10:1--10:28", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1455026806", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kortchemski:2016:TSL, author = "Igor Kortchemski and Cyril Marzouk", title = "Triangulating stable laminations", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "11:1--11:31", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1455559938", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bally:2016:AMS, author = "Vlad Bally and Cl{\'e}ment Rey", title = "Approximation of {Markov} semigroups in total variation distance", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "12:1--12:44", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1455717196", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Taggi:2016:ASP, author = "Lorenzo Taggi", title = "Absorbing-state phase transition in biased activated random walk", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "13:1--13:15", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1456246244", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Engelke:2016:LDP, author = "Sebastian Engelke and Jevgenijs Ivanovs", title = "A {L{\'e}vy}-derived process seen from its supremum and max-stable processes", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "14:1--14:19", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1456246245", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bhattacharjee:2016:SES, author = "Chinmoy Bhattacharjee and Larry Goldstein", title = "On strong embeddings by {Stein}'s method", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "15:1--15:30", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1456412955", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ahn:2016:OQS, author = "Sung Won Ahn and Jonathon Peterson", title = "Oscillations of quenched slowdown asymptotics for ballistic one-dimensional random walk in a random environment", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "16:1--16:27", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1456412956", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Evilsizor:2016:EGL, author = "Stephen Evilsizor and Nicolas Lanchier", title = "Evolutionary games on the lattice: death--birth updating process", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "17:1--17:29", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1456412957", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Berglund:2016:RSR, author = "Nils Berglund and Christian Kuehn", title = "Regularity structures and renormalisation of {FitzHugh--Nagumo} {SPDEs} in three space dimensions", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "18:1--18:48", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See corrigendum \cite{Berglund:2019:CRS}.", URL = "https://projecteuclid.org/euclid.ejp/1456412958", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Asselah:2016:DLD, author = "Amine Asselah and Emilio N. M. Cirillo and Benedetto Scoppola and Elisabetta Scoppola", title = "On diffusion limited deposition", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "19:1--19:29", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1456499641", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pinelis:2016:OBP, author = "Iosif Pinelis", title = "Optimal binomial, {Poisson}, and normal left-tail domination for sums of nonnegative random variables", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "20:1--20:19", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1457706456", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Mossel:2016:CTP, author = "Elchanan Mossel and Joe Neeman and Allan Sly", title = "Consistency thresholds for the planted bisection model", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "21:1--21:24", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1457706457", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Trevisan:2016:WPM, author = "Dario Trevisan", title = "Well-posedness of multidimensional diffusion processes with weakly differentiable coefficients", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "22:1--22:41", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1458325000", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kyprianou:2016:DFS, author = "Andreas E. Kyprianou", title = "Deep factorisation of the stable process", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "23:1--23:28", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1459880111", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Auffinger:2016:TCH, author = "Antonio Auffinger and Si Tang", title = "On the time constant of high dimensional first passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "24:1--24:23", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1459880112", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Webb:2016:LSC, author = "Christian Webb", title = "Linear statistics of the circular $ \beta $-ensemble, {Stein}'s method, and circular {Dyson} {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "25:1--25:16", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1459960919", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ferrario:2016:CLS, author = "Benedetta Ferrario", title = "Characterization of the law for {$3$D} stochastic hyperviscous fluids", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "26:1--26:22", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1459960920", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Disertori:2016:CNS, author = "Margherita Disertori and Franz Merkl and Silke W. W. Rolles", title = "A comparison of a nonlinear sigma model with general pinning and pinning at one point", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "27:1--27:16", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1460141798", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pain:2016:VBB, author = "Michel Pain", title = "Velocity of the {$L$}-branching {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "28:1--28:28", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1460652929", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Caputo:2016:DLT, author = "Pietro Caputo and Fabio Martinelli and Alistair Sinclair and Alexandre Stauffer", title = "Dynamics of lattice triangulations on thin rectangles", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "29:1--29:22", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1460652930", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Lin:2016:NAP, author = "Jeff Lin", title = "A negative answer to a problem of {Aldous} on determination of exchangeable sequences", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "30:1--30:26", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1460652931", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Mourrat:2016:PTC, author = "Jean-Christophe Mourrat and Daniel Valesin", title = "Phase transition of the contact process on random regular graphs", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "31:1--31:17", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1460652932", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Augeri:2016:LDP, author = "Fanny Augeri", title = "Large deviations principle for the largest eigenvalue of {Wigner} matrices without {Gaussian} tails", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "32:1--32:49", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1461007173", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Andres:2016:HKE, author = "Sebastian Andres and Jean-Dominique Deuschel and Martin Slowik", title = "Heat kernel estimates for random walks with degenerate weights", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "33:1--33:21", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1461007174", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Inahama:2016:STK, author = "Yuzuru Inahama", title = "Short time kernel asymptotics for rough differential equation driven by fractional {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "34:1--34:29", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1461332875", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Sznitman:2016:CAL, author = "Alain-Sol Sznitman", title = "Coupling and an application to level-set percolation of the {Gaussian} free field", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "35:1--35:26", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1461332876", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bouchard:2016:GDM, author = "Bruno Bouchard and Dylan Possama{\"\i} and Xiaolu Tan", title = "A general {Doob--Meyer--Mertens} decomposition for $g$-supermartingale systems", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "36:1--36:21", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1462192627", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bakhtin:2016:IBE, author = "Yuri Bakhtin", title = "Inviscid {Burgers} equation with random kick forcing in noncompact setting", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "37:1--37:50", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1463683782", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Birkner:2016:RWD, author = "Matthias Birkner and Ji{\v{r}}{\'\i} {\v{C}}ern{\'y} and Andrej Depperschmidt", title = "Random walks in dynamic random environments and ancestry under local population regulation", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "38:1--38:43", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1464269713", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dolgopyat:2016:LLT, author = "Dmitry Dolgopyat", title = "A {Local Limit Theorem} for sums of independent random vectors", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "39:1--39:15", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1465991837", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Mukherjee:2016:FPC, author = "Sumit Mukherjee", title = "Fixed points and cycle structure of random permutations", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "40:1--40:18", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1465991838", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Drapeau:2016:SMP, author = "Samuel Drapeau and Christoph Mainberger", title = "Stability and {Markov} property of forward backward minimal supersolutions", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "41:1--41:15", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Jun 20 10:21:16 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1466166072", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Addario-Berry:2016:RWC, author = "Louigi Addario-Berry and Roberto I. Oliveira and Yuval Peres and Perla Sousi", title = "Random walks colliding before getting trapped", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "42:1--42:19", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1469199632", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Durieu:2016:IUS, author = "Olivier Durieu and Yizao Wang", title = "From infinite urn schemes to decompositions of self-similar {Gaussian} processes", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "43:1--43:23", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1469557136", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hermon:2016:TVS, author = "Jonathan Hermon and Hubert Lacoin and Yuval Peres", title = "Total variation and separation cutoffs are not equivalent and neither one implies the other", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "44:1--44:36", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1469557137", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Forsstrom:2016:MPE, author = "Malin Pal{\"o} Forsstr{\"o}m", title = "Monotonicity properties of exclusion sensitivity", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "45:1--45:22", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1469557138", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pinsky:2016:TRG, author = "Ross G. Pinsky", title = "Transience\slash recurrence and growth rates for diffusion processes in time-dependent regions", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "46:1--46:24", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1469557139", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Jansen:2016:CPG, author = "Sabine Jansen", title = "Continuum percolation for {Gibbsian} point processes with attractive interactions", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "47:1--47:22", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1469720442", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Baurdoux:2016:OPP, author = "Erik J. Baurdoux and Andreas E. Kyprianou and Curdin Ott", title = "Optimal prediction for positive self-similar {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "48:1--48:24", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1469720443", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Carmona:2016:IPD, author = "Philippe Carmona and Nicolas P{\'e}tr{\'e}lis", title = "Interacting partially directed self avoiding walk: scaling limits", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "49:1--49:52", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1469720444", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Jagannath:2016:ODB, author = "Aukosh Jagannath", title = "On the overlap distribution of Branching Random Walks", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "50:1--50:16", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1470316405", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Haji-Mirsadeghi:2016:STB, author = "Mir-Omid Haji-Mirsadeghi and Ali Khezeli", title = "Stable transports between stationary random measures", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "51:1--51:25", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1470414022", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Donati-Martin:2016:NEE, author = "Catherine Donati-Martin and Alain Rouault", title = "Near-extreme eigenvalues in the beta-ensembles", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "52:1--52:17", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1472142775", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Champagnat:2016:MFS, author = "Nicolas Champagnat and Henry Benoit", title = "Moments of the frequency spectrum of a splitting tree with neutral {Poissonian} mutations", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "53:1--53:34", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1472830615", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dieuleveut:2016:USP, author = "Daphn{\'e} Dieuleveut", title = "The {UIPQ} seen from a point at infinity along its geodesic ray", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "54:1--54:44", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1473188081", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Piaggio:2016:EZE, author = "Mat{\'\i}as Carrasco Piaggio and Pablo Lessa", title = "Equivalence of zero entropy and the {Liouville} property for stationary random graphs", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "55:1--55:24", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1473188082", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Duse:2016:CAP, author = "Erik Duse and Kurt Johansson and Anthony Metcalfe", title = "The Cusp-{Airy} process", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "57:1--57:50", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1473424498", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Veraar:2016:CCM, author = "Mark Veraar and Ivan Yaroslavtsev", title = "Cylindrical continuous martingales and stochastic integration in infinite dimensions", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "59:1--59:53", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1475266507", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fajfrova:2016:IMM, author = "Lucie Fajfrov{\'a} and Thierry Gobron and Ellen Saada", title = "Invariant measures of mass migration processes", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "60:1--60:52", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1475266508", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Greven:2016:FTS, author = "Andreas Greven and Peter Pfaffelhuber and Cornelia Pokalyuk and Anton Wakolbinger", title = "The fixation time of a strongly beneficial allele in a structured population", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "61:1--61:42", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1475586182", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Iksanov:2016:LUR, author = "Alexander Iksanov and Zakhar Kabluchko and Alexander Marynych", title = "Local universality for real roots of random trigonometric polynomials", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "63:1--63:19", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1476706888", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dumitrescu:2016:GDG, author = "Roxana Dumitrescu and Marie-Claire Quenez and Agn{\`e}s Sulem", title = "Generalized {Dynkin} games and doubly reflected {BSDEs} with jumps", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "64:1--64:32", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Nov 5 09:05:31 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1477395747", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Damron:2016:ERE, author = "Michael Damron and Xuan Wang", title = "Entropy reduction in {Euclidean} first-passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "65:1--65:23", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1479524422", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Alexander:2016:LLT, author = "Kenneth S. Alexander and Quentin Berger", title = "Local limit theorems and renewal theory with no moments", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "66:1--66:18", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1480129233", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Englander:2016:BDP, author = "J{\'a}nos Engl{\"a}nder and Liang Zhang", title = "Branching diffusion with particle interactions", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "67:1--67:25", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1480388424", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Alexander:2016:LAF, author = "Kenneth S. Alexander and Quentin Berger", title = "Local asymptotics for the first intersection of two independent renewals", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "68:1--68:20", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1480561217", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Blondel:2016:CSB, author = "Oriane Blondel and Patr{\'\i}cia Gon{\c{c}}alves and Marielle Simon", title = "Convergence to the stochastic {Burgers} equation from a degenerate microscopic dynamics", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "69:1--69:25", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1480561218", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kosygina:2016:FLL, author = "Elena Kosygina and Jonathon Peterson", title = "Functional limit laws for recurrent excited random walks with periodic cookie stacks", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "70:1--70:24", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1480688087", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bethuelsen:2016:ACW, author = "Stein Andreas Bethuelsen and Florian V{\"o}llering", title = "Absolute continuity and weak uniform mixing of random walk in dynamic random environment", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "71:1--71:32", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1480688088", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Matzavinos:2016:RWS, author = "Anastasios Matzavinos and Alexander Roitershtein and Youngsoo Seol", title = "Random walks in a sparse random environment", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "72:1--72:20", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1480993226", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Butez:2016:LDE, author = "Rapha{\"e}l Butez", title = "Large deviations for the empirical measure of random polynomials: revisit of the {Zeitouni--Zelditch} theorem", journal = j-ELECTRON-J-PROBAB, volume = "21", number = "??", pages = "73:1--73:37", month = "????", year = "2016", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:12 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1481079628", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Jarvenpaa:2017:HPR, author = "Esa J{\"a}rvenp{\"a}{\"a} and Maarit J{\"a}rvenp{\"a}{\"a} and Henna Koivusalo and Bing Li and Ville Suomala and Yimin Xiao", title = "Hitting probabilities of random covering sets in tori and metric spaces", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "1:1--1:18", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1483585523", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dobler:2017:QJT, author = "Christian D{\"o}bler and Giovanni Peccati", title = "Quantitative {de Jong} theorems in any dimension", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "2:1--2:35", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1483585524", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kouritzin:2017:ENF, author = "Michael A. Kouritzin and Wei Sun and Jie Xiong", title = "Erratum: Nonlinear filtering for reflecting diffusions in random environments via nonparametric estimation", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "3:1--3:2", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Kouritzin:2004:NFR}.", URL = "https://projecteuclid.org/euclid.ejp/1483585525", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ortgiese:2017:OPL, author = "Marcel Ortgiese and Matthew I. Roberts", title = "One-point localization for branching random walk in {Pareto} environment", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "6:1--6:20", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1484622023", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Grothaus:2017:SDE, author = "Martin Grothaus and Robert Vo{\ss}hall", title = "Stochastic differential equations with sticky reflection and boundary diffusion", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "7:1--7:37", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1485486107", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Budhiraja:2017:UTI, author = "Amarjit Budhiraja and Wai-Tong Louis Fan", title = "Uniform in time interacting particle approximations for nonlinear equations of {Patlak--Keller--Segel} type", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "8:1--8:37", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1485831704", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Morris:2017:MTF, author = "Ben Morris and Anastasia Raymer", title = "Mixing time of the fifteen puzzle", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "9:1--9:29", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1485831705", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Feldheim:2017:DRR, author = "Ohad N. Feldheim and Arnab Sen", title = "Double roots of random polynomials with integer coefficients", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "10:1--10:23", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1486090890", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Junnila:2017:UCG, author = "Janne Junnila and Eero Saksman", title = "Uniqueness of critical {Gaussian} chaos", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "11:1--11:31", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1486090891", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Peres:2017:IMT, author = "Yuval Peres and Thomas Sauerwald and Perla Sousi and Alexandre Stauffer", title = "Intersection and mixing times for reversible chains", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "12:1--12:16", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1486090892", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Corwin:2017:IDD, author = "Ivan Corwin and Mihai Nica", title = "Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "13:1--13:49", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1486090893", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kolb:2017:CSD, author = "Martin Kolb and Mladen Savov", title = "Conditional survival distributions of {Brownian} trajectories in a one dimensional {Poissonian} environment in the critical case", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "14:1--14:29", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1487127642", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Shi:2017:GFP, author = "Quan Shi", title = "Growth-fragmentation processes and bifurcators", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "15:1--15:25", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1487127643", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dhara:2017:CWC, author = "Souvik Dhara and Remco van der Hofstad and Johan S. H. van Leeuwaarden and Sanchayan Sen", title = "Critical window for the configuration model: finite third moment degrees", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "16:1--16:33", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1487127644", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Owada:2017:FCL, author = "Takashi Owada", title = "Functional central limit theorem for subgraph counting processes", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "17:1--17:38", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1487127645", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Johnson:2017:LLF, author = "Tobias Johnson and Anne Schilling and Erik Slivken", title = "Local limit of the fixed point forest", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "18:1--18:26", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1487127646", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Konarovskyi:2017:ABM, author = "Vitalii Konarovskyi", title = "On asymptotic behavior of the modified {Arratia} flow", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "19:1--19:31", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1487386997", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Haas:2017:AHR, author = "B{\'e}n{\'e}dicte Haas", title = "Asymptotics of heights in random trees constructed by aggregation", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "21:1--21:25", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1487646307", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Nemish:2017:LLP, author = "Yuriy Nemish", title = "Local law for the product of independent non-{Hermitian} random matrices with independent entries", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "22:1--22:35", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1487991681", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kifer:2017:FER, author = "Yuri Kifer", title = "Functional {Erd{\H{o}}s--R{\'e}nyi} law of large numbers for nonconventional sums under weak dependence", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "23:1--23:17", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1488337348", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Riedel:2017:TCI, author = "Sebastian Riedel", title = "Transportation-cost inequalities for diffusions driven by {Gaussian} processes", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "24:1--24:26", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1488596710", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Alt:2017:LLR, author = "Johannes Alt and L{\'a}szl{\'o} Erd{\H{o}}s and Torben Kr{\"u}ger", title = "Local law for random {Gram} matrices", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "25:1--25:41", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 11 16:32:13 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1488942016", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Mailler:2017:MVP, author = "C{\'e}cile Mailler and Jean-Fran{\c{c}}ois Marckert", title = "Measure-valued {P{\'o}lya} urn processes", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "26:1--26:33", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1490061796", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dadoun:2017:ASS, author = "Benjamin Dadoun", title = "Asymptotics of self-similar growth-fragmentation processes", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "27:1--27:30", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1490061797", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gu:2017:GGF, author = "Yu Gu and Jean-Christophe Mourrat", title = "On generalized {Gaussian} free fields and stochastic homogenization", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "28:1--28:21", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1490320844", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gravner:2017:BPP, author = "Janko Gravner and David Sivakoff", title = "Bootstrap percolation on products of cycles and complete graphs", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "29:1--29:20", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1490320845", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Che:2017:URM, author = "Ziliang Che", title = "Universality of random matrices with correlated entries", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "30:1--30:38", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1490320846", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Arnaudon:2017:RBM, author = "Marc Arnaudon and Xue-Mei Li", title = "Reflected {Brownian} motion: selection, approximation and linearization", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "31:1--31:55", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1490407496", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Levy:2017:FDI, author = "Avi Levy", title = "Finitely dependent insertion processes", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "32:1--32:19", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1491962643", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Sidoravicius:2017:AST, author = "Vladas Sidoravicius and Augusto Teixeira", title = "Absorbing-state transition for {Stochastic Sandpiles} and {Activated Random Walks}", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "33:1--33:35", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1492070448", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Newman:2017:PVM, author = "C. M. Newman and K. Ravishankar and E. Schertzer", title = "Perturbations of {Voter} model in one-dimension", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "34:1--34:42", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1492502428", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Budd:2017:GIP, author = "Timothy Budd and Nicolas Curien", title = "Geometry of infinite planar maps with high degrees", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "35:1--35:37", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1492588824", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Carmesin:2017:LHS, author = "Johannes Carmesin and Bruno Federici and Agelos Georgakopoulos", title = "A {Liouville} hyperbolic souvlaki", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "36:1--36:19", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1493085635", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Schweinsberg:2017:RRPa, author = "Jason Schweinsberg", title = "Rigorous results for a population model with selection {I}: evolution of the fitness distribution", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "37:1--37:94", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1493258436", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Schweinsberg:2017:RRPb, author = "Jason Schweinsberg", title = "Rigorous results for a population model with selection {II}: genealogy of the population", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "38:1--38:54", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1493258437", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Erbar:2017:RCB, author = "Matthias Erbar and Christopher Henderson and Georg Menz and Prasad Tetali", title = "{Ricci} curvature bounds for weakly interacting {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "40:1--40:23", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1493345027", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Berglund:2017:EKL, author = "Nils Berglund and Giacomo {Di Ges{\`u}} and Hendrik Weber", title = "An {Eyring--Kramers} law for the stochastic {Allen--Cahn} equation in dimension two", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "41:1--41:27", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1493345028", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chevallier:2017:FMF, author = "Julien Chevallier", title = "Fluctuations for mean-field interacting age-dependent {Hawkes} processes", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "42:1--42:49", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1493777018", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pitman:2017:EGS, author = "Jim Pitman and Yuri Yakubovich", title = "Extremes and gaps in sampling from a {GEM} random discrete distribution", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "44:1--44:26", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1493777020", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gwynne:2017:SLC, author = "Ewain Gwynne and Xin Sun", title = "Scaling limits for the critical {Fortuin--Kasteleyn} model on a random planar map {II}: local estimates and empty reduced word exponent", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "45:1--45:56", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1494036159", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Konakov:2017:WEE, author = "Valentin Konakov and St{\'e}phane Menozzi", title = "Weak error for the {Euler} scheme approximation of diffusions with non-smooth coefficients", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "46:1--46:47", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1494489631", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Seuret:2017:MAO, author = "St{\'e}phane Seuret and Xiaochuan Yang", title = "Multifractal analysis for the occupation measure of stable-like processes", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "47:1--47:36", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1496109646", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fedrizzi:2017:RSK, author = "Ennio Fedrizzi and Franco Flandoli and Enrico Priola and Julien Vovelle", title = "Regularity of stochastic kinetic equations", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "48:1--48:42", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1496196076", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gouere:2017:PTC, author = "Jean-Baptiste Gou{\'e}r{\'e} and Marie Th{\'e}ret", title = "Positivity of the time constant in a continuous model of first passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "49:1--49:21", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1496196077", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Aldous:2017:EPU, author = "David Aldous and Russell Lyons", title = "Errata to ``{Processes on unimodular random networks}''", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "51:1--51:4", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Aldous:2007:PUR,Aldous:2019:SEP}.", URL = "https://projecteuclid.org/euclid.ejp/1498010464", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Groux:2017:AFR, author = "Benjamin Groux", title = "Asymptotic freeness for rectangular random matrices and large deviations for sample covariance matrices with sub-{Gaussian} tails", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "53:1--53:40", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1498010466", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Forrester:2017:MBE, author = "Peter J. Forrester and Dong Wang", title = "{Muttalib--Borodin} ensembles in random matrix theory --- realisations and correlation functions", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "54:1--54:43", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1498183245", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hu:2017:HML, author = "Wenqing Hu and Konstantinos Spiliopoulos{\"\i}", title = "Hypoelliptic multiscale {Langevin} diffusions: large deviations, invariant measures and small mass asymptotics", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "55:1--55:38", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 4 09:55:45 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1498809677", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Sarantsev:2017:SGD, author = "Andrey Sarantsev and Li-Cheng Tsai", title = "Stationary gap distributions for infinite systems of competing {Brownian} particles", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "56:1--56:20", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1499220068", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Rassoul-Agha:2017:AVQ, author = "Firas Rassoul-Agha and Timo Sepp{\"a}l{\"a}inen and Atilla Yilmaz", title = "Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "57:1--57:47", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1499306456", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chen:2017:LBB, author = "Xinxin Chen and Gr{\'e}gory Miermont", title = "Long {Brownian} bridges in hyperbolic spaces converge to {Brownian} trees", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "58:1--58:15", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1500516020", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Angst:2017:WCC, author = "J{\"u}rgen Angst and Guillaume Poly", title = "A weak {Cram{\'e}r} condition and application to {Edgeworth} expansions", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "59:1--59:24", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1500516021", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Xi:2017:LCL, author = "Haokai Xi and Fan Yang and Jun Yin", title = "Local circular law for the product of a deterministic matrix with a random matrix", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "60:1--60:77", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1500602612", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Auffinger:2017:DPS, author = "Antonio Auffinger and Wei-Kuo Chen", title = "A duality principle in spin glasses", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "61:1--61:17", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1500689052", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Samson:2017:TEI, author = "Paul-Marie Samson", title = "Transport-entropy inequalities on locally acting groups of permutations", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "62:1--62:33", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1502244025", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fehrman:2017:ELI, author = "Benjamin Fehrman", title = "Exit laws of isotropic diffusions in random environment from large domains", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "63:1--63:37", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1502330523", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bourgade:2017:ESS, author = "Paul Bourgade and Jiaoyang Huang and Horng-Tzer Yau", title = "Eigenvector statistics of sparse random matrices", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "64:1--64:38", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1502417019", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chen:2017:SAP, author = "Xia Chen and Yaozhong Hu and David Nualart and Samy Tindel", title = "Spatial asymptotics for the parabolic {Anderson} model driven by a {Gaussian} rough noise", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "65:1--65:38", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Aug 24 18:58:04 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1503367245", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Petrelis:2017:SLU, author = "Nicolas P{\'e}tr{\'e}lis and Rongfeng Sun and Niccol{\`o} Torri", title = "Scaling limit of the uniform prudent walk", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "66:1--66:19", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1504749661", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gantert:2017:BRW, author = "Nina Gantert and Stefan Junk", title = "A branching random walk among disasters", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "67:1--67:34", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1504922530", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chandra:2017:MBS, author = "Ajay Chandra and Hao Shen", title = "Moment bounds for {SPDEs} with non-{Gaussian} fields and application to the {Wong-Zakai} problem", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "68:1--68:32", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1504922531", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kotani:2017:PSD, author = "Shinichi Kotani and Fumihiko Nakano", title = "{Poisson} statistics for $1$ d {Schr{\"o}dinger} operators with random decaying potentials", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "69:1--69:31", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1504922532", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bianchi:2017:MRI, author = "Alessandra Bianchi and Sander Dommers and Cristian Giardin{\`a}", title = "Metastability in the reversible inclusion process", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "70:1--70:34", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1505268101", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Deng:2017:HIS, author = "Chang-Song Deng and Ren{\'e} L. Schilling", title = "{Harnack} inequalities for {SDEs} driven by time-changed fractional {Brownian} motions", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "71:1--71:23", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1505268102", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gomez:2017:UBP, author = "Alejandro Gomez and Jong Jun Lee and Carl Mueller and Eyal Neuman and Michael Salins", title = "On uniqueness and blowup properties for a class of second order {SDEs}", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "72:1--72:17", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1505268103", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kumar:2017:EAL, author = "Chaman Kumar and Sotirios Sabanis", title = "On explicit approximations for {L{\'e}vy} driven {SDEs} with super-linear diffusion coefficients", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "73:1--73:19", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1505268104", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Reddy:2017:LED, author = "Tulasi Ram Reddy", title = "Limiting empirical distribution of zeros and critical points of random polynomials agree in general", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "74:1--74:18", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1505268105", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Damron:2017:CDC, author = "Michael Damron and Jack Hanson and Philippe Sosoe", title = "On the chemical distance in critical percolation", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "75:1--75:43", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1505354464", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Muller:2017:PLD, author = "Patrick E. M{\"u}ller", title = "Path large deviations for interacting diffusions with local mean-field interactions in random environment", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "76:1--76:56", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1505527232", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dereich:2017:DSF, author = "Steffen Dereich and Christian M{\"o}nch and Peter M{\"o}rters", title = "Distances in scale free networks at criticality", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "77:1--77:38", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1506931227", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Garet:2017:CTI, author = "Olivier Garet and R{\'e}gine Marchand and Eviatar B. Procaccia and Marie Th{\'e}ret", title = "Continuity of the time and isoperimetric constants in supercritical percolation", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "78:1--78:35", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1506931228", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ferrari:2017:HET, author = "Patrik L. Ferrari and B{\'a}lint Vet{\H{o}}", title = "The hard-edge tacnode process for {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "79:1--79:32", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1506931229", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Broutin:2017:RCT, author = "Nicolas Broutin and Minmin Wang", title = "Reversing the cut tree of the {Brownian} continuum random tree", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "80:1--80:23", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1507255394", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Holmes:2017:CBI, author = "Mark Holmes and Thomas S. Salisbury", title = "Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "81:1--81:18", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1507536148", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Croydon:2017:TCS, author = "David Croydon and Ben Hambly and Takashi Kumagai", title = "Time-changes of stochastic processes associated with resistance forms", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "82:1--82:41", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1507795233", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Martin:2017:RRM, author = "James B. Martin and Bal{\'a}zs R{\'a}th", title = "Rigid representations of the multiplicative coalescent with linear deletion", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "83:1--83:47", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1507946758", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gwynne:2017:SLU, author = "Ewain Gwynne and Jason Miller", title = "Scaling limit of the uniform infinite half-plane quadrangulation in the {Gromov--Hausdorff--Prokhorov}-uniform topology", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "84:1--84:47", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1507946759", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dhara:2017:PTE, author = "Souvik Dhara and Debankur Mukherjee and Subhabrata Sen", title = "Phase transitions of extremal cuts for the configuration model", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "86:1--86:29", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1507946761", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Krokowski:2017:MCL, author = "Kai Krokowski and Christoph Th{\"a}le", title = "Multivariate central limit theorems for {Rademacher} functionals with applications", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "87:1--87:30", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1508292258", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Berger:2017:NPL, author = "Noam Berger and Ran J. Tessler", title = "No percolation in low temperature spin glass", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "88:1--88:19", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1508292259", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Wu:2017:BAE, author = "Hao Wu and Dapeng Zhan", title = "Boundary arm exponents for {SLE}", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "89:1--89:26", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1508292260", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hough:2017:MCC, author = "Robert Hough", title = "Mixing and cut-off in cycle walks", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "90:1--90:49", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1508292261", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Miclo:2017:DHO, author = "Laurent Miclo", title = "Duality and hypoellipticity: one-dimensional case studies", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "91:1--91:32", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1508464837", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Guerra:2017:ADR, author = "Enrique Guerra and Alejandro F. Ram{\'\i}rez", title = "Asymptotic direction for random walks in mixing random environments", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "92:1--92:41", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1508810545", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{David:2017:RLQ, author = "Fran{\c{c}}ois David and Antti Kupiainen and R{\'e}mi Rhodes and Vincent Vargas", title = "Renormalizability of {Liouville} quantum field theory at the {Seiberg} bound", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "93:1--93:26", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1509501716", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gao:2017:LTA, author = "Fuqing Gao", title = "Long time asymptotics of unbounded additive functionals of {Markov} processes", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "94:1--94:21", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1509501717", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pagnard:2017:LLM, author = "Camille Pagnard", title = "Local limits of {Markov} branching trees and their volume growth", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "95:1--95:53", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1510110478", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dobler:2017:ITB, author = "Christian D{\"o}bler and Robert E. Gaunt and Sebastian J. Vollmer", title = "An iterative technique for bounding derivatives of solutions of {Stein} equations", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "96:1--96:39", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1510802250", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Furlan:2017:TCR, author = "Marco Furlan and Jean-Christophe Mourrat", title = "A tightness criterion for random fields, with application to the {Ising} model", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "97:1--97:29", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1510802251", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Butkovsky:2017:IMS, author = "Oleg Butkovsky and Michael Scheutzow", title = "Invariant measures for stochastic functional differential equations", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "98:1--98:23", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1510802252", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Grama:2017:HML, author = "Ion Grama and Quansheng Liu and Eric Miqueu", title = "Harmonic moments and large deviations for a supercritical branching process in a random environment", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "99:1--99:23", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1510802253", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hutchcroft:2017:BPG, author = "Tom Hutchcroft and Yuval Peres", title = "Boundaries of planar graphs: a unified approach", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "100:1--100:20", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1511578855", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Nguyen:2017:ESN, author = "Gia Bao Nguyen and Daniel Remenik", title = "Extreme statistics of non-intersecting {Brownian} paths", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "102:1--102:40", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1511773232", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Etheridge:2017:BBM, author = "Alison Etheridge and Nic Freeman and Sarah Penington", title = "Branching {Brownian} motion, mean curvature flow and the motion of hybrid zones", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "103:1--103:40", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1512615692", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hoshino:2017:SCG, author = "Masato Hoshino and Yuzuru Inahama and Nobuaki Naganuma", title = "Stochastic complex {Ginzburg--Landau} equation with space-time white noise", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "104:1--104:68", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1513349792", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hirsch:2017:PCP, author = "Christian Hirsch and Tim Brereton and Volker Schmidt", title = "Percolation and convergence properties of graphs related to minimal spanning forests", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "105:1--105:21", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1514430041", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Beringer:2017:PCP, author = "Dorottya Beringer and G{\'a}bor Pete and {\'A}d{\'a}m Tim{\'a}r", title = "On percolation critical probabilities and unimodular random graphs", journal = j-ELECTRON-J-PROBAB, volume = "22", number = "??", pages = "106:1--106:26", month = "????", year = "2017", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:57 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1514430042", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Janson:2018:CPP, author = "Svante Janson and Lutz Warnke", title = "On the critical probability in percolation", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "1:1--1:25", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Jan 12 16:29:59 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1515726029", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bouguet:2018:FEM, author = "Florian Bouguet and Bertrand Cloez", title = "Fluctuations of the empirical measure of freezing {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "2:1--2:31", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1516093310", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pinsky:2018:SDA, author = "Ross G. Pinsky", title = "On the strange domain of attraction to generalized {Dickman} distributions for sums of independent random variables", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "3:1--3:17", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1516093311", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Privault:2018:SAF, author = "Nicolas Privault and Grzegorz Serafin", title = "{Stein} approximation for functionals of independent random sequences", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "4:1--4:34", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1517367680", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ross:2018:SLS, author = "Nathan Ross and Yuting Wen", title = "Scaling limits for some random trees constructed inhomogeneously", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "5:1--5:35", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1517626965", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Alexander:2018:PRQ, author = "Kenneth S. Alexander and Quentin Berger", title = "Pinning of a renewal on a quenched renewal", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "6:1--6:48", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1518426053", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Lambert:2018:MFU, author = "Gaultier Lambert", title = "Mesoscopic fluctuations for unitary invariant ensembles", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "7:1--7:33", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1518426054", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Juillet:2018:MAP, author = "Nicolas Juillet", title = "Martingales associated to peacocks using the curtain coupling", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "8:1--8:29", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1518426055", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Grote:2018:ASC, author = "Julian Grote and Elisabeth Werner", title = "Approximation of smooth convex bodies by random polytopes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "9:1--9:21", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1518426057", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kuznetsov:2018:SAS, author = "Alexey Kuznetsov and Mateusz Kwa{\'s}nicki", title = "Spectral analysis of stable processes on the positive half-line", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "10:1--10:29", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1518426058", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bogdan:2018:YLS, author = "Krzysztof Bogdan and Zbigniew Palmowski and Longmin Wang", title = "{Yaglom} limit for stable processes in cones", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "11:1--11:19", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1518426059", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{denHollander:2018:EED, author = "F. den Hollander and M. Mandjes and A. Roccaverde and N. J. Starreveld", title = "Ensemble equivalence for dense graphs", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "12:1--12:26", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1518426060", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kuhn:2018:MPF, author = "Franziska K{\"u}hn", title = "On martingale problems and {Feller} processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "13:1--13:18", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1518426061", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chen:2018:TAF, author = "Xia Chen and Yaozhong Hu and Jian Song and Xiaoming Song", title = "Temporal asymptotics for fractional parabolic {Anderson} model", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "14:1--14:39", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519182022", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dette:2018:URM, author = "Holger Dette and Dominik Tomecki and Martin Venker", title = "Universality in Random Moment Problems", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "15:1--15:23", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519354944", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Mossel:2018:NSC, author = "Elchanan Mossel and Joe Neeman", title = "Noise stability and correlation with half spaces", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "16:1--16:17", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519354945", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hermon:2018:FT, author = "Jonathan Hermon", title = "Frogs on trees?", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "17:1--17:40", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519354946", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Banerjee:2018:CNR, author = "Debapratim Banerjee", title = "Contiguity and non-reconstruction results for planted partition models: the dense case", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "18:1--18:28", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519354947", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Baccelli:2018:PSF, author = "Fran{\c{c}}ois Baccelli and Mir-Omid Haji-Mirsadeghi", title = "Point-shift foliation of a point process", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "19:1--19:25", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519354948", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Cheng:2018:ESM, author = "Li-Juan Cheng and Anton Thalmaier", title = "Evolution systems of measures and semigroup properties on evolving manifolds", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "20:1--20:27", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519722149", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Collet:2018:PSM, author = "Francesca Collet and Richard C. Kraaij", title = "Path-space moderate deviation principles for the random field {Curie--Weiss} model", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "21:1--21:45", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519722150", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hambly:2018:EST, author = "Ben Hambly and Weiye Yang", title = "Existence and space-time regularity for stochastic heat equations on p.c.f. fractals", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "22:1--22:30", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519722151", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ren:2018:WDS, author = "Yan-Xia Ren and Renming Song and Rui Zhang", title = "{Williams} decomposition for superprocesses", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "23:1--23:33", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519722152", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Banerjee:2018:CPS, author = "Sayan Banerjee and Wilfrid Kendall", title = "Coupling polynomial {Stratonovich} integrals: the two-dimensional {Brownian} case", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "24:1--24:43", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1519722153", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hermon:2018:SMT, author = "Jonathan Hermon and Yuval Peres", title = "On sensitivity of mixing times and cutoff", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "25:1--25:34", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1521079338", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bernstein:2018:RWS, author = "Megan Bernstein", title = "A random walk on the symmetric group generated by random involutions", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "26:1--26:28", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1521079339", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Zerner:2018:RTC, author = "Martin P. W. Zerner", title = "Recurrence and transience of contractive autoregressive processes and related {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "27:1--27:24", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1521079340", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Debussche:2018:SES, author = "Arnaud Debussche and Hendrik Weber", title = "The {Schr{\"o}dinger} equation with spatial white noise potential", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "28:1--28:16", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1522375268", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kruhner:2018:APC, author = "Paul Kr{\"u}hner and Martin Larsson", title = "Affine processes with compact state space", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "29:1--29:23", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1522375269", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bates:2018:LDP, author = "Erik Bates", title = "Localization of directed polymers with general reference walk", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "30:1--30:45", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1522375270", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Powell:2018:CGC, author = "Ellen Powell", title = "Critical {Gaussian} chaos: convergence and uniqueness in the derivative normalisation", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "31:1--31:26", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1522375271", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Zhai:2018:ECC, author = "Alex Zhai", title = "Exponential concentration of cover times", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "32:1--32:22", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1523325625", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Basak:2018:CLS, author = "Anirban Basak and Nicholas Cook and Ofer Zeitouni", title = "Circular law for the sum of random permutation matrices", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "33:1--33:51", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1524880977", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Janson:2018:MCB, author = "Svante Janson and Nicolas Pouyanne", title = "Moment convergence of balanced {P{\'o}lya} processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "34:1--34:13", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1524880978", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Eldan:2018:DMF, author = "Ronen Eldan and Renan Gross", title = "Decomposition of mean-field {Gibbs} distributions into product measures", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "35:1--35:24", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1524880979", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dobler:2018:FMT, author = "Christian D{\"o}bler and Anna Vidotto and Guangqu Zheng", title = "Fourth moment theorems on the {Poisson} space in any dimension", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "36:1--36:27", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525312960", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Coupier:2018:SNS, author = "David Coupier", title = "Sublinearity of the number of semi-infinite branches for geometric random trees", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "37:1--37:33", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525852814", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chaumont:2018:CSD, author = "Hans Chaumont and Christian Noack", title = "Characterizing stationary $ 1 + 1 $ dimensional lattice polymer models", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "38:1--38:19", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525852815", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{LeGoff:2018:VRN, author = "Line C. {Le Goff} and Olivier Raimond", title = "Vertex reinforced non-backtracking random walks: an example of path formation", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "39:1--39:38", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525852816", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Abe:2018:ELT, author = "Yoshihiro Abe", title = "Extremes of local times for simple random walks on symmetric trees", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "40:1--40:41", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525852817", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gufler:2018:REC, author = "Stephan Gufler", title = "A representation for exchangeable coalescent trees and generalized tree-valued {Fleming--Viot} processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "41:1--41:42", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525852818", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gufler:2018:PCT, author = "Stephan Gufler", title = "Pathwise construction of tree-valued {Fleming--Viot} processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "42:1--42:58", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525852819", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Travers:2018:ERW, author = "Nicholas F. Travers", title = "Excited random walk in a {Markovian} environment", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "43:1--43:60", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525852820", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bahadoran:2018:QEF, author = "C. Bahadoran and T. Bodineau", title = "Quantitative estimates for the flux of {TASEP} with dilute site disorder", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "44:1--44:44", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1525852821", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bally:2018:CDN, author = "Vlad Bally and Lucia Caramellino and Guillaume Poly", title = "Convergence in distribution norms in the {CLT} for non identical distributed random variables", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "45:1--45:51", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1527213726", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Rousselin:2018:IMH, author = "Pierre Rousselin", title = "Invariant measures, {Hausdorff} dimension and dimension drop of some harmonic measures on {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "46:1--46:31", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1527213727", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fan:2018:NSC, author = "Wai-Tong (Louis) Fan and Sebastien Roch", title = "Necessary and sufficient conditions for consistent root reconstruction in {Markov} models on trees", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "47:1--47:24", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1527213728", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Birkner:2018:CRD, author = "Matthias Birkner and Huili Liu and Anja Sturm", title = "Coalescent results for diploid exchangeable population models", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "49:1--49:44", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1527818427", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ferrari:2018:UGT, author = "Patrik L. Ferrari and Alessandra Occelli", title = "Universality of the {GOE} {Tracy--Widom} distribution for {TASEP} with arbitrary particle density", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "51:1--51:24", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1527818429", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chen:2018:RGB, author = "Dayue Chen and Yueyun Hu and Shen Lin", title = "Resistance growth of branching random networks", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "52:1--52:17", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1527818430", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gold:2018:IIG, author = "Julian Gold", title = "Intrinsic isoperimetry of the giant component of supercritical bond percolation in dimension two", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "53:1--53:41", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1527818431", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Baur:2018:UIH, author = "Erich Baur and Lo{\"\i}c Richier", title = "Uniform infinite half-planar quadrangulations with skewness", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "54:1--54:43", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1528358488", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Cuneo:2018:NES, author = "No{\'e} Cuneo and Jean-Pierre Eckmann and Martin Hairer and Luc Rey-Bellet", title = "Non-equilibrium steady states for networks of oscillators", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "55:1--55:28", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1528358489", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chevyrev:2018:SDT, author = "Ilya Chevyrev and Marcel Ogrodnik", title = "A support and density theorem for {Markovian} rough paths", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "56:1--56:16", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1528704074", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gheissari:2018:EBC, author = "Reza Gheissari and Eyal Lubetzky", title = "The effect of boundary conditions on mixing of {$2$D} {Potts} models at discontinuous phase transitions", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "57:1--57:30", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1528704075", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Marcus:2018:SPP, author = "Michael B. Marcus and Jay Rosen", title = "Sample path properties of permanental processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "58:1--58:47", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1528704076", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Cortines:2018:DFS, author = "Aser Cortines and Julian Gold and Oren Louidor", title = "Dynamical freezing in a spin glass system with logarithmic correlations", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "59:1--59:31", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1528704077", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pitman:2018:APR, author = "Jim Pitman and Wenpin Tang", title = "The argmin process of random walks, {Brownian} motion and {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "60:1--60:35", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1529460158", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Aru:2018:TVL, author = "Juhan Aru and Avelio Sep{\'u}lveda", title = "Two-valued local sets of the {$2$D} continuum {Gaussian} free field: connectivity, labels, and induced metrics", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "61:1--61:35", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1529460159", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kim:2018:EDH, author = "Panki Kim and Ante Mimica", title = "Estimates of {Dirichlet} heat kernels for subordinate {Brownian} motions", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "64:1--64:45", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532570592", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Crisan:2018:PRS, author = "Dan Crisan and Christopher Janjigian and Thomas G. Kurtz", title = "Particle representations for stochastic partial differential equations with boundary conditions", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "65:1--65:29", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532570593", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Schertzer:2018:HCP, author = "Emmanuel Schertzer and Florian Simatos", title = "Height and contour processes of {Crump-Mode-Jagers} forests ({I}): general distribution and scaling limits in the case of short edges", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "67:1--67:43", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532570595", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Flegel:2018:LPD, author = "Franziska Flegel", title = "Localization of the principal {Dirichlet} eigenvector in the heavy-tailed random conductance model", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "68:1--68:43", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532570596", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Maller:2018:MNS, author = "Ross A. Maller and David M. Mason", title = "Matrix normalised stochastic compactness for a {L{\'e}vy} process at zero", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "69:1--69:37", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532570597", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{vonSoosten:2018:PTU, author = "Per von Soosten and Simone Warzel", title = "The phase transition in the ultrametric ensemble and local stability of {Dyson} {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "70:1--70:24", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532570598", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chetwynd-Diggle:2018:SMS, author = "Jonathan A. Chetwynd-Diggle and Alison M. Etheridge", title = "{SuperBrownian} motion and the spatial {Lambda--Fleming--Viot} process", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "71:1--71:36", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532570599", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Baar:2018:PES, author = "Martina Baar and Anton Bovier", title = "The polymorphic evolution sequence for populations with phenotypic plasticity", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "72:1--72:27", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532678635", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dembo:2018:CLC, author = "Amir Dembo and Takashi Kumagai and Chikara Nakamura", title = "Cutoff for lamplighter chains on fractals", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "73:1--73:21", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532678636", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dolinsky:2018:NSD, author = "Yan Dolinsky and Benjamin Gottesman", title = "Numerical scheme for {Dynkin} games under model uncertainty", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "74:1--74:20", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532678637", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Patie:2018:BGF, author = "Pierre Patie and Mladen Savov", title = "{Bernstein}-gamma functions and exponential functionals of {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "75:1--75:101", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1532678638", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Au:2018:TDR, author = "Benson Au", title = "Traffic distributions of random band matrices", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "77:1--77:48", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717736", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Joyner:2018:RWA, author = "Christopher H. Joyner and Uzy Smilansky", title = "A random walk approach to linear statistics in random tournament ensembles", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "80:1--80:37", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717739", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{vandeBrug:2018:SSL, author = "Tim van de Brug and Federico Camia and Marcin Lis", title = "Spin systems from loop soups", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "81:1--81:17", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717740", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Galanis:2018:USA, author = "Andreas Galanis and Leslie Ann Goldberg and Kuan Yang", title = "Uniqueness for the $3$-state antiferromagnetic {Potts} model on the tree", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "82:1--82:43", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717741", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Georgiou:2018:DRT, author = "Nicos Georgiou and Davar Khoshnevisan and Kunwoo Kim and Alex D. Ramos", title = "The dimension of the range of a transient random walk", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "83:1--83:31", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717742", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Costantini:2018:EUR, author = "Cristina Costantini and Thomas G. Kurtz", title = "Existence and uniqueness of reflecting diffusions in cusps", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "84:1--84:21", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717743", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Holcomb:2018:RMH, author = "Diane Holcomb", title = "The random matrix hard edge: rare events and a transition", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "85:1--85:20", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717744", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Collevecchio:2018:SOR, author = "Andrea Collevecchio and Mark Holmes and Daniel Kious", title = "On the speed of once-reinforced biased random walk on trees", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "86:1--86:32", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717745", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Delmas:2018:CFL, author = "Jean-Fran{\c{c}}ois Delmas and Jean-St{\'e}phane Dhersin and Marion Sciauveau", title = "Cost functionals for large (uniform and simply generated) random trees", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "87:1--87:36", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717746", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Richier:2018:IIC, author = "Lo{\"\i}c Richier", title = "The incipient infinite cluster of the uniform infinite half-planar triangulation", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "89:1--89:38", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717748", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Devulder:2018:CSW, author = "Alexis Devulder and Nina Gantert and Fran{\c{c}}oise P{\`e}ne", title = "Collisions of several walkers in recurrent random environments", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "90:1--90:34", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717749", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{DelMoral:2018:SCE, author = "Pierre {Del Moral} and Aline Kurtzmann and Julian Tugaut", title = "On the stability and the concentration of extended {Kalman--Bucy} filters", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "91:1--91:30", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536717750", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bobkov:2018:BEB, author = "S. G. Bobkov and G. P. Chistyakov and F. G{\"o}tze", title = "{Berry--Esseen} bounds for typical weighted sums", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "92:1--92:22", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1536976980", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Feray:2018:WDG, author = "Valentin F{\'e}ray", title = "Weighted dependency graphs", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "93:1--93:65", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1537257885", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Blancas:2018:TWT, author = "Airam Blancas and Jean-Jil Duchamps and Amaury Lambert and Arno Siri-J{\'e}gousse", title = "Trees within trees: simple nested coalescents", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "94:1--94:27", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1537257886", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Landim:2018:MMC, author = "Claudio Landim and Michail Loulakis and Mustapha Mourragui", title = "Metastable {Markov} chains: from the convergence of the trace to the convergence of the finite-dimensional distributions", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "95:1--95:34", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1537322680", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Duminil-Copin:2018:URC, author = "Hugo Duminil-Copin and Jhih-Huang Li and Ioan Manolescu", title = "Universality for the random-cluster model on isoradial graphs", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "96:1--96:70", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1537322681", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{denHollander:2018:MHC, author = "Frank den Hollander and Francesca R. Nardi and Siamak Taati", title = "Metastability of hard-core dynamics on bipartite graphs", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "97:1--97:65", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1537495434", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Felipe:2018:BPS, author = "Miraine D{\'a}vila Felipe and Amaury Lambert", title = "Branching processes seen from their extinction time via path decompositions of reflected {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "98:1--98:30", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1537841130", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Rossignol:2018:ECF, author = "Rapha{\"e}l Rossignol and Marie Th{\'e}ret", title = "Existence and continuity of the flow constant in first passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "99:1--99:42", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1537927580", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Goldstein:2018:NAD, author = "Larry Goldstein", title = "Non-asymptotic distributional bounds for the {Dickman} approximation of the running time of the {Quickselect} algorithm", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "100:1--100:13", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1538445816", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Arizmendi:2018:LTF, author = "Octavio Arizmendi and Takahiro Hasebe", title = "Limit theorems for free {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "101:1--101:36", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1538618571", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Basak:2018:DLP, author = "Anirban Basak and Rick Durrett and Eric Foxall", title = "Diffusion limit for the partner model at the critical value", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "102:1--102:42", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1539309901", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Benoist:2018:NPS, author = "St{\'e}phane Benoist", title = "Natural parametrization of {SLE}: the {Gaussian} free field point of view", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "103:1--103:16", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1539828067", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Beckman:2018:ABB, author = "Erin Beckman and Emily Dinan and Rick Durrett and Ran Huo and Matthew Junge", title = "Asymptotic behavior of the {Brownian} frog model", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "104:1--104:19", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540000928", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Nitzschner:2018:DLS, author = "Maximilian Nitzschner", title = "Disconnection by level sets of the discrete {Gaussian} free field and entropic repulsion", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "105:1--105:21", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540260051", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Assiotis:2018:RSG, author = "Theodoros Assiotis", title = "Random surface growth and {Karlin--McGregor} polynomials", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "106:1--106:81", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540260052", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Durieu:2018:FRS, author = "Olivier Durieu and Yizao Wang", title = "A family of random sup-measures with long-range dependence", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "107:1--107:24", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540260053", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ahlberg:2018:NSV, author = "Daniel Ahlberg and Rangel Baldasso", title = "Noise sensitivity and {Voronoi} percolation", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "108:1--108:21", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540865371", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hong:2018:RLT, author = "Jieliang Hong", title = "Renormalization of local times of super-{Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "109:1--109:45", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540865372", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Cook:2018:NHR, author = "Nicholas Cook and Walid Hachem and Jamal Najim and David Renfrew", title = "Non-{Hermitian} random matrices with a variance profile ({I}): deterministic equivalents and limiting {ESDs}", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "110:1--110:61", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540865373", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dubach:2018:PGE, author = "Guillaume Dubach", title = "Powers of {Ginibre} eigenvalues", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "111:1--111:31", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540865374", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Budhiraja:2018:LDS, author = "Amarjit Budhiraja and Paul Dupuis and Arnab Ganguly", title = "Large deviations for small noise diffusions in a fast {Markovian} environment", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "112:1--112:33", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1540951492", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Romito:2018:SME, author = "Marco Romito", title = "A simple method for the existence of a density for stochastic evolutions with rough coefficients", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "113:1--113:43", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1542942364", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Buraczewski:2018:PLD, author = "Dariusz Buraczewski and Piotr Dyszewski", title = "Precise large deviations for random walk in random environment", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "114:1--114:26", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1542942365", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Levajkovic:2018:SEE, author = "Tijana Levajkovi{\'c} and Stevan Pilipovi{\'c} and Dora Sele{\v{s}}i and Milica {\v{Z}}igi{\'c}", title = "Stochastic evolution equations with {Wick}-polynomial nonlinearities", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "116:1--116:25", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1543028704", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Muller:2018:RAC, author = "Noela M{\"u}ller and Ralph Neininger", title = "Refined asymptotics for the composition of cyclic urns", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "117:1--117:20", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1543028707", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kammoun:2018:MSD, author = "Mohamed Slim Kammoun", title = "Monotonous subsequences and the descent process of invariant random permutations", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "118:1--118:31", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1543287754", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Daletskii:2018:SDE, author = "Alexei Daletskii", title = "Stochastic differential equations in a scale of {Hilbert} spaces", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "119:1--119:15", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1544843299", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Lambert:2018:TOM, author = "Amaury Lambert and Ger{\'o}nimo Uribe Bravo", title = "Totally ordered measured trees and splitting trees with infinite variation", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "120:1--120:41", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1544843300", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Papapantoleon:2018:EUR, author = "Antonis Papapantoleon and Dylan Possama{\"\i} and Alexandros Saplaouras", title = "Existence and uniqueness results for {BSDE} with jumps: the whole nine yards", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "121:1--121:68", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545102139", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Barbour:2018:CLT, author = "A. D. Barbour and Adrian R{\"o}llin", title = "A central limit theorem for the gossip process", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "123:1--123:37", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545102141", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Marx:2018:NAC, author = "Victor Marx", title = "A new approach for the construction of a {Wasserstein} diffusion", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "124:1--124:54", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545188691", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Criens:2018:ACS, author = "David Criens and Kathrin Glau", title = "Absolute continuity of semimartingales", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "125:1--125:28", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545188692", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Foxall:2018:NGC, author = "Eric Foxall", title = "The naming game on the complete graph", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "126:1--126:42", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545188693", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hartung:2018:PDC, author = "Lisa Hartung and Anton Klimovsky", title = "The phase diagram of the complex branching {Brownian} motion energy model", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "127:1--127:27", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545188694", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Qian:2018:LPP, author = "Wei Qian and Wendelin Werner", title = "The law of a point process of {Brownian} excursions in a domain is determined by the law of its trace", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "128:1--128:23", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545210235", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Sethuraman:2018:HLL, author = "Sunder Sethuraman and Doron Shahar", title = "Hydrodynamic limits for long-range asymmetric interacting particle systems", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "130:1--130:54", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545361594", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{McRedmond:2018:CHP, author = "James McRedmond and Andrew R. Wade", title = "The convex hull of a planar random walk: perimeter, diameter, and shape", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "131:1--131:24", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545447916", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bauer:2018:SSM, author = "Martin Bauer and Thilo Meyer-Brandis and Frank Proske", title = "Strong solutions of mean-field stochastic differential equations with irregular drift", journal = j-ELECTRON-J-PROBAB, volume = "23", number = "??", pages = "132:1--132:35", month = "????", year = "2018", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:29 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1545447917", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Blondel:2019:FEF, author = "Oriane Blondel and Aurelia Deshayes and Cristina Toninelli", title = "Front evolution of the {Fredrickson--Andersen} one spin facilitated model", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "1:1--1:32", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1546571126", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Devroye:2019:HSG, author = "Luc Devroye and Cecilia Holmgren and Henning Sulzbach", title = "Heavy subtrees of {Galton--Watson} trees with an application to {Apollonian} networks", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "2:1--2:44", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1549357219", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Imkeller:2019:DSD, author = "Peter Imkeller and Gon{\c{c}}alo dos Reis and William Salkeld", title = "Differentiability of {SDEs} with drifts of super-linear growth", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "3:1--3:43", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1549616424", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Harter:2019:SAS, author = "Jonathan Harter and Adrien Richou", title = "A stability approach for solving multidimensional quadratic {BSDEs}", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "4:1--4:51", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1549616425", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ged:2019:PSS, author = "Fran{\c{c}}ois Gaston Ged", title = "Profile of a self-similar growth-fragmentation", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "7:1--7:21", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550199785", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Safikhani:2019:SCE, author = "Abolfazl Safikhani and Yimin Xiao", title = "Spectral conditions for equivalence of {Gaussian} random fields with stationary increments", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "8:1--8:19", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550199786", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Che:2019:ULS, author = "Ziliang Che and Patrick Lopatto", title = "Universality of the least singular value for sparse random matrices", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "9:1--9:53", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550221265", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Jaramillo:2019:CES, author = "Arturo Jaramillo and Juan Carlos Pardo and Jos{\'e} Luis P{\'e}rez", title = "Convergence of the empirical spectral distribution of {Gaussian} matrix-valued processes", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "10:1--10:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550286034", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Habermann:2019:STF, author = "Karen Habermann", title = "Small-time fluctuations for the bridge in a model class of hypoelliptic diffusions of weak {H{\"o}rmander} type", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "11:1--11:19", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550480425", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Jourdain:2019:NAE, author = "Benjamin Jourdain and Ahmed Kebaier", title = "Non-asymptotic error bounds for the multilevel {Monte Carlo} {Euler} method applied to {SDEs} with constant diffusion coefficient", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "12:1--12:34", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550653271", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Tanguy:2019:NAV, author = "Kevin Tanguy", title = "Non asymptotic variance bounds and deviation inequalities by optimal transport", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "13:1--13:18", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550653272", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Lin:2019:CSW, author = "Kevin Lin and Carl Mueller", title = "Can the stochastic wave equation with strong drift hit zero?", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "14:1--14:26", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550653273", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Abraham:2019:APE, author = "Romain Abraham and Jean-Fran{\c{c}}ois Delmas", title = "Asymptotic properties of expansive {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "15:1--15:51", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550826098", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Olla:2019:ELD, author = "Stefano Olla and Li-Cheng Tsai", title = "Exceedingly large deviations of the totally asymmetric exclusion process", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "16:1--16:71", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1550826099", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Profeta:2019:CES, author = "Christophe Profeta and Thomas Simon", title = "{Cram{\'e}r}'s estimate for stable processes with power drift", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "17:1--17:21", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1551150461", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Lugosi:2019:FSU, author = "G{\'a}bor Lugosi and Alan S. Pereira", title = "Finding the seed of uniform attachment trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "18:1--18:15", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1551323285", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bansaye:2019:SLP, author = "Vincent Bansaye and Maria-Emilia Caballero and Sylvie M{\'e}l{\'e}ard", title = "Scaling limits of population and evolution processes in random environment", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "19:1--19:38", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Sat Mar 16 10:33:33 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1552013626", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Coupier:2019:DCR, author = "David Coupier and Jean-Fran{\c{c}}ois Marckert and Viet Chi Tran", title = "Directed, cylindric and radial {Brownian} webs", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "20:1--20:48", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553133829", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Unterberger:2019:GFL, author = "Jeremie Unterberger", title = "Global fluctuations for {$1$D} log-gas dynamics. Covariance kernel and support", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "21:1--21:28", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553155301", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Schmid:2019:MTS, author = "Dominik Schmid", title = "Mixing times for the simple exclusion process in ballistic random environment", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "22:1--22:25", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553155302", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Lubbers:2019:SCB, author = "Jan-Erik L{\"u}bbers and Matthias Meiners", title = "The speed of critically biased random walk in a one-dimensional percolation model", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "23:1--23:29", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553306439", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hug:2019:STS, author = "Daniel Hug and Christoph Th{\"a}le", title = "Splitting tessellations in spherical spaces", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "24:1--24:60", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553565775", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Aldous:2019:SEP, author = "David Aldous and Russell Lyons", title = "Second Errata to {``Processes on Unimodular Random Networks''}", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "25:1--25:2", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Aldous:2007:PUR,Aldous:2017:EPU}.", URL = "https://projecteuclid.org/euclid.ejp/1553565776", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Eberle:2019:QCR, author = "Andreas Eberle and Mateusz B. Majka", title = "Quantitative contraction rates for {Markov} chains on general state spaces", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "26:1--26:36", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553565777", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Barbour:2019:MAT, author = "A. D. Barbour and A. Xia", title = "Multivariate approximation in total variation using local dependence", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "27:1--27:35", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553565778", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ben-Ari:2019:RWC, author = "Iddo Ben-Ari and Alexander Roitershtein and Rinaldo B. Schinazi", title = "A random walk with catastrophes", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "28:1--28:21", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553565779", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Arras:2019:SMMa, author = "Benjamin Arras and Christian Houdr{\'e}", title = "On {Stein}'s method for multivariate self-decomposable laws with finite first moment", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "29:1--29:33", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553565780", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Cuchiero:2019:PMV, author = "Christa Cuchiero and Martin Larsson and Sara Svaluto-Ferro", title = "Probability measure-valued polynomial diffusions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "30:1--30:32", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1553565781", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Michelen:2019:IPG, author = "Marcus Michelen and Robin Pemantle and Josh Rosenberg", title = "Invasion percolation on {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "31:1--31:35", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554256913", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Benjamini:2019:RSC, author = "Itai Benjamini and Jonathan Hermon", title = "Rapid social connectivity", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "32:1--32:33", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554775411", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Foucart:2019:CSB, author = "Cl{\'e}ment Foucart", title = "Continuous-state branching processes with competition: duality and reflection at infinity", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "33:1--33:38", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554775412", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kabluchko:2019:DBZ, author = "Zakhar Kabluchko and Hauke Seidel", title = "Distances between zeroes and critical points for random polynomials with i.i.d. zeroes", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "34:1--34:25", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554775413", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fang:2019:WBN, author = "Xiao Fang", title = "{Wasserstein}-2 bounds in normal approximation under local dependence", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "35:1--35:14", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554775414", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chen:2019:RWD, author = "Yu-Ting Chen", title = "Rescaled {Whittaker} driven stochastic differential equations converge to the additive stochastic heat equation", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "36:1--36:33", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554775415", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Caputo:2019:CBP, author = "Pietro Caputo and Dmitry Ioffe and Vitali Wachtel", title = "Confinement of {Brownian} polymers under geometric area tilts", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "37:1--37:21", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554775416", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Avena:2019:RWC, author = "Luca Avena and Yuki Chino and Conrado da Costa and Frank den Hollander", title = "Random walk in cooling random environment: ergodic limits and concentration inequalities", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "38:1--38:35", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554775418", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Vanneuville:2019:ASR, author = "Hugo Vanneuville", title = "Annealed scaling relations for {Voronoi} percolation", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "39:1--39:71", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1554861841", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kwasnicki:2019:FTL, author = "Mateusz Kwa{\'s}nicki", title = "Fluctuation theory for {L{\'e}vy} processes with completely monotone jumps", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "40:1--40:40", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1555034439", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Marcovici:2019:ESC, author = "Ir{\`e}ne Marcovici and Mathieu Sablik and Siamak Taati", title = "Ergodicity of some classes of cellular automata subject to noise", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "41:1--41:44", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1555034440", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Adamczak:2019:NCP, author = "Rados{\l}aw Adamczak and Micha{\l} Kotowski and Bart{\l}omiej Polaczyk and Micha{\l} Strzelecki", title = "A note on concentration for polynomials in the {Ising} model", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "42:1--42:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1555466612", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Meliot:2019:ART, author = "Pierre-Lo{\"\i}c M{\'e}liot", title = "Asymptotic representation theory and the spectrum of a random geometric graph on a compact {Lie} group", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "43:1--43:85", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1555466613", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Adhikari:2019:EUC, author = "Arka Adhikari and Ziliang Che", title = "Edge universality of correlated {Gaussians}", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "44:1--44:25", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1556179228", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Sun:2019:ALU, author = "Wen Sun and Robert Philippe", title = "Analysis of large urn models with local mean-field interactions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "45:1--45:33", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1557453644", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Berger:2019:SRT, author = "Quentin Berger", title = "Strong renewal theorems and local large deviations for multivariate random walks and renewals", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "46:1--46:47", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1557453645", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Schertzer:2019:HCP, author = "Emmanuel Schertzer and Florian Simatos", title = "Height and contour processes of {Crump--Mode--Jagers} forests {(II)}: the {Bellman--Harris} universality class", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "47:1--47:38", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1558145015", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Georgiou:2019:IPN, author = "Nicholas Georgiou and Aleksandar Mijatovi{\'c} and Andrew R. Wade", title = "Invariance principle for non-homogeneous random walks", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "48:1--48:38", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1558145016", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hammond:2019:SAP, author = "Alan Hammond", title = "On self-avoiding polygons and walks: the snake method via polygon joining", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "49:1--49:43", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1558404407", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Delarue:2019:MEM, author = "Fran{\c{c}}ois Delarue and Daniel Lacker and Kavita Ramanan", title = "From the master equation to mean field game limit theory: a central limit theorem", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "51:1--51:54", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1558576902", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Glode:2019:BTC, author = "Patric Gl{\"o}de and Andreas Greven and Thomas Rippl", title = "Branching trees {I}: concatenation and infinite divisibility", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "52:1--52:55", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1559354444", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hughes:2019:BLT, author = "Thomas Hughes", title = "A boundary local time for one-dimensional super-{Brownian} motion and applications", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "54:1--54:58", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1559700304", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Doring:2019:LPF, author = "Leif D{\"o}ring and Alexander R. Watson and Philip Weissmann", title = "{L{\'e}vy} processes with finite variance conditioned to avoid an interval", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "55:1--55:32", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1559700305", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hong:2019:ABH, author = "Wenming Hong and Xiaoyue Zhang", title = "Asymptotic behaviour of heavy-tailed branching processes in random environments", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "56:1--56:17", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1559700306", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Forien:2019:SSM, author = "Rapha{\"e}l Forien", title = "The stepping stone model in a random environment and the effect of local heterogeneities on isolation by distance patterns", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "57:1--57:35", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1560391565", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gwynne:2019:HFM, author = "Ewain Gwynne and Jason Miller and Scott Sheffield", title = "Harmonic functions on mated-{CRT} maps", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "58:1--58:55", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561082667", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Brault:2019:NLS, author = "Antoine Brault and Antoine Lejay", title = "The non-linear sewing lemma {I}: weak formulation", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "59:1--59:24", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561082668", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dalang:2019:RFS, author = "Robert C. Dalang and Thomas Humeau", title = "Random field solutions to linear {SPDEs} driven by symmetric pure jump {L{\'e}vy} space-time white noises", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "60:1--60:28", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561082669", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Olvera-Cravioto:2019:CPD, author = "Mariana Olvera-Cravioto", title = "Convergence of the population dynamics algorithm in the {Wasserstein} metric", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "61:1--61:27", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561082670", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Georgiou:2019:MCH, author = "Nicholas Georgiou and Mikhail V. Menshikov and Dimitri Petritis and Andrew R. Wade", title = "{Markov} chains with heavy-tailed increments and asymptotically zero drift", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "62:1--62:28", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561082671", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{DeMasi:2019:NLB, author = "Anna {De Masi} and Pablo A. Ferrari and Errico Presutti and Nahuel Soprano-Loto", title = "Non local branching {Brownian} motions with annihilation and free boundary problems", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "63:1--63:30", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561082672", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Milos:2019:EPT, author = "Piotr Mi{\l}o{\'s} and Bat{\i} {\c{S}}eng{\"u}l", title = "Existence of a phase transition of the interchange process on the {Hamming} graph", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "64:1--64:21", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561169148", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Sakai:2019:SMH, author = "Akira Sakai and Gordon Slade", title = "Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "65:1--65:18", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561169149", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ankirchner:2019:SEC, author = "Stefan Ankirchner and Nabil Kazi-Tani and Maike Klein and Thomas Kruse", title = "Stopping with expectation constraints: 3 points suffice", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "66:1--66:16", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561687599", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fill:2019:QIR, author = "James Allen Fill and Wei-Chun Hung", title = "{QuickSort}: improved right-tail asymptotics for the limiting distribution, and large deviations", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "67:1--67:13", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561687600", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hilario:2019:STS, author = "Marcelo Hilario and Xinyi Li and Petr Panov", title = "Shape theorem and surface fluctuation for {Poisson} cylinders", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "68:1--68:16", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561687601", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Buraczewski:2019:RWM, author = "Dariusz Buraczewski and Piotr Dyszewski and Alexander Iksanov and Alexander Marynych and Alexander Roitershtein", title = "Random walks in a moderately sparse random environment", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "69:1--69:44", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561687602", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Lupu:2019:ICS, author = "Titus Lupu and Christophe Sabot and Pierre Tarr{\`e}s", title = "Inverting the coupling of the signed {Gaussian} free field with a loop-soup", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "70:1--70:28", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561687603", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dalmao:2019:PSC, author = "Federico Dalmao and Ivan Nourdin and Giovanni Peccati and Maurizia Rossi", title = "Phase singularities in complex arithmetic random waves", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "71:1--71:45", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561687604", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Caravenna:2019:LLD, author = "Francesco Caravenna and Ron Doney", title = "Local large deviations and the strong renewal theorem", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "72:1--72:48", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561687605", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Connor:2019:MTE, author = "Stephen B. Connor and Richard J. Pymar", title = "Mixing times for exclusion processes on hypergraphs", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "73:1--73:48", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1561687606", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Betz:2019:SLB, author = "Volker Betz and Lorenzo Taggi", title = "Scaling limit of ballistic self-avoiding walk interacting with spatial random permutations", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "74:1--74:37", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1562119474", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Venet:2019:NFB, author = "Nil Venet", title = "Nonexistence of fractional {Brownian} fields indexed by cylinders", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "75:1--75:26", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1562119475", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Can:2019:FPT, author = "Van Hao Can and Shuta Nakajima", title = "First passage time of the frog model has a sublinear variance", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "76:1--76:27", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1562292237", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Baumler:2019:UNU, author = "Johannes B{\"a}umler", title = "Uniqueness and non-uniqueness for spin-glass ground states on trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "77:1--77:17", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1563264040", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Shi:2019:PTC, author = "Quan Shi and Alexander R. Watson", title = "Probability tilting of compensated fragmentations", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "78:1--78:39", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1565057003", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Basse-OConnor:2019:LTF, author = "Andreas Basse-O'Connor and Claudio Heinrich and Mark Podolskij", title = "On limit theory for functionals of stationary increments {L{\'e}vy} driven moving averages", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "79:1--79:42", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1567648850", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Blondel:2019:RWR, author = "Oriane Blondel and Marcelo R. Hil{\'a}rio and Renato S. dos Santos and Vladas Sidoravicius and Augusto Teixeira", title = "Random walk on random walks: higher dimensions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "80:1--80:33", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1567670466", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bandini:2019:BRR, author = "Elena Bandini and Fulvia Confortola and Andrea Cosso", title = "{BSDE} representation and randomized dynamic programming principle for stochastic control problems of infinite-dimensional jump-diffusions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "81:1--81:37", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568080857", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pinsky:2019:ODD, author = "Ross G. Pinsky", title = "Optimizing the drift in a diffusive search for a random stationary target", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "82:1--82:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568080861", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bishop:2019:SMV, author = "Adrian N. Bishop and Pierre {Del Moral}", title = "On the stability of matrix-valued {Riccati} diffusions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "84:1--84:40", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568080863", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gotze:2019:HOC, author = "Friedrich G{\"o}tze and Holger Sambale and Arthur Sinulis", title = "Higher order concentration for functions of weakly dependent random variables", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "85:1--85:19", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568080865", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Budzinski:2019:SCM, author = "Thomas Budzinski", title = "Supercritical causal maps: geodesics and simple random walk", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "86:1--86:43", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568080866", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Biskup:2019:IPO, author = "Marek Biskup", title = "An invariance principle for one-dimensional random walks among dynamical random conductances", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "87:1--87:29", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568080867", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dorsch:2019:RPH, author = "Florian Dorsch and Hermann Schulz-Baldes", title = "Random perturbations of hyperbolic dynamics", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "89:1--89:23", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568080869", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Christoph:2019:DPH, author = "Hofer-Temmel Christoph", title = "Disagreement percolation for the hard-sphere model", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "91:1--91:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568080871", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Denisov:2019:ACH, author = "Denis Denisov and Vitali Wachtel", title = "Alternative constructions of a harmonic function for a random walk in a cone", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "92:1--92:26", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568253841", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Versendaal:2019:LDG, author = "Rik Versendaal", title = "Large deviations for geodesic random walks", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "93:1--93:39", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568361634", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Johnston:2019:GGW, author = "Samuel G. G. Johnston", title = "The genealogy of {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "94:1--94:35", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568361635", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Frikha:2019:IPF, author = "Noufel Frikha and Arturo Kohatsu-Higa and Libo Li", title = "Integration by parts formula for killed processes: a point of view from approximation theory", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "95:1--95:44", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568793788", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bourgade:2019:GFD, author = "Paul Bourgade and Krishnan Mody", title = "{Gaussian} fluctuations of the determinant of {Wigner} matrices", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "96:1--96:28", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568793789", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bartl:2019:SID, author = "Daniel Bartl and Michael Kupper and Ariel Neufeld", title = "Stochastic integration and differential equations for typical paths", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "97:1--97:21", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568793790", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Laruelle:2019:NRU, author = "Sophie Laruelle and Gilles Pag{\`e}s", title = "Nonlinear randomized urn models: a stochastic approximation viewpoint", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "98:1--98:47", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568793792", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Boutaud:2019:RPS, author = "Pierre Boutaud and Pascal Maillard", title = "A revisited proof of the {Seneta--Heyde} norming for branching random walks under optimal assumptions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "99:1--99:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568793793", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Devulder:2019:AMW, author = "Alexis Devulder and Nina Gantert and Fran{\c{c}}oise P{\`e}ne", title = "Arbitrary many walkers meet infinitely often in a subballistic random environment", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "100:1--100:25", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568793794", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Caravenna:2019:DSR, author = "Francesco Caravenna and Rongfeng Sun and Nikos Zygouras", title = "The {Dickman} subordinator, renewal theorems, and disordered systems", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "101:1--101:40", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1568793795", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Suzuki:2019:CBM, author = "Kohei Suzuki", title = "Convergence of {Brownian} motions on metric measure spaces under {Riemannian} Curvature--Dimension conditions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "102:1--102:36", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1569463328", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Foucart:2019:CCS, author = "Cl{\'e}ment Foucart and Chunhua Ma and Bastien Mallein", title = "Coalescences in continuous-state branching processes", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "103:1--103:52", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1569895472", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Henning:2019:GGM, author = "Florian Henning and Christof K{\"u}lske and Arnaud {Le Ny} and Utkir A. Rozikov", title = "Gradient {Gibbs} measures for the {SOS} model with countable values on a {Cayley} tree", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "104:1--104:23", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1569895473", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hu:2019:HCS, author = "Yaozhong Hu and David Nualart and Panqiu Xia", title = "{H{\"o}lder} continuity of the solutions to a class of {SPDE's} arising from branching particle systems in a random environment", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "105:1--105:52", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1569895474", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Balan:2019:EDS, author = "Raluca M. Balan and Llu{\'\i}s Quer-Sardanyons and Jian Song", title = "Existence of density for the stochastic wave equation with space-time homogeneous {Gaussian} noise", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "106:1--106:43", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1569895475", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Strzelecka:2019:ENL, author = "Marta Strzelecka", title = "Estimates of norms of log-concave random matrices with dependent entries", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "107:1--107:15", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1569981822", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bjornberg:2019:IPR, author = "Jakob E. Bj{\"o}rnberg and Micha{\l} Kotowski and Benjamin Lees and Piotr Mi{\l}o{\'s}", title = "The interchange process with reversals on the complete graph", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "108:1--108:43", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1569981823", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Eisenbaum:2019:DID, author = "Nathalie Eisenbaum", title = "Decompositions of infinitely divisible nonnegative processes", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "109:1--109:25", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1569981824", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Alves:2019:DIS, author = "Caio Alves and Artem Sapozhnikov", title = "Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "110:1--110:34", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1570068174", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Li:2019:OPF, author = "Xinyi Li and Daisuke Shiraishi", title = "One-point function estimates for loop-erased random walk in three dimensions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "111:1--111:46", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1570586691", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hoffman:2019:ISF, author = "Christopher Hoffman and Tobias Johnson and Matthew Junge", title = "Infection spread for the frog model on trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "112:1--112:29", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1570586692", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Berglund:2019:CRS, author = "Nils Berglund and Christian Kuehn", title = "Corrigendum to {``Regularity structures and renormalisation of FitzHugh--Nagumo SPDEs in three space dimensions''}", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "113:1--113:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Berglund:2016:RSR}.", URL = "https://projecteuclid.org/euclid.ejp/1570672858", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Adams:2019:WRM, author = "Stefan Adams and Michael Eyers", title = "The {Widom--Rowlinson} model on the {Delaunay} graph", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "114:1--114:41", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1570759239", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Schiavo:2019:CFD, author = "Lorenzo Dello Schiavo", title = "Characteristic functionals of {Dirichlet} measures", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "115:1--115:38", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1570759240", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Flint:2019:FIM, author = "Ian Flint and Nicolas Privault and Giovanni Luca Torrisi", title = "Functional inequalities for marked point processes", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "116:1--116:40", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1570759241", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Perkowski:2019:KER, author = "Nicolas Perkowski and Tommaso Cornelis Rosati", title = "The {KPZ} equation on the real line", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "117:1--117:56", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1572314777", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Chen:2019:DBP, author = "Le Chen and Jingyu Huang and Davar Khoshnevisan and Kunwoo Kim", title = "Dense blowup for parabolic {SPDEs}", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "118:1--118:33", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1572314778", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Nualart:2019:AES, author = "David Nualart and Nakahiro Yoshida", title = "Asymptotic expansion of {Skorohod} integrals", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "119:1--119:64", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1572508843", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Baccelli:2019:DT, author = "Fran{\c{c}}ois Baccelli and Mir-Omid Haji-Mirsadeghi and James T. {Murphy III}", title = "{Doeblin} trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "120:1--120:36", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573009611", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Collevecchio:2019:BRN, author = "Andrea Collevecchio and Cong Bang Huynh and Daniel Kious", title = "The branching-ruin number as critical parameter of random processes on trees", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "121:1--121:29", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573030842", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Aleandri:2019:ODL, author = "Michele Aleandri and Ida G. Minelli", title = "Opinion dynamics with {Lotka--Volterra} type interactions", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "122:1--122:31", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573030843", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Yang:2019:EUS, author = "Fan Yang", title = "Edge universality of separable covariance matrices", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "123:1--123:57", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573030844", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Varvenne:2019:CIS, author = "Maylis Varvenne", title = "Concentration inequalities for Stochastic Differential Equations with additive fractional noise", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "124:1--124:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573268588", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Janson:2019:HPR, author = "Svante Janson", title = "The hiring problem with rank-based strategies", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "125:1--125:35", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573268589", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hillion:2019:PSO, author = "Erwan Hillion and Oliver Johnson", title = "A proof of the {Shepp--Olkin} entropy monotonicity conjecture", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "126:1--126:14", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573268590", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ramirez:2019:NEB, author = "Alejandro F. Ram{\'\i}rez and Santiago Saglietti", title = "New examples of ballistic {RWRE} in the low disorder regime", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "127:1--127:20", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573268591", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Arras:2019:SMMb, author = "Benjamin Arras and Christian Houdr{\'e}", title = "On {Stein}'s method for multivariate self-decomposable laws", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "128:1--128:63", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573268592", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Shang:2019:TCI, author = "Shijie Shang and Tusheng Zhang", title = "{Talagrand} concentration inequalities for stochastic heat-type equations under uniform distance", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "129:1--129:15", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573527858", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Schulte:2019:MSO, author = "Matthias Schulte and J. E. Yukich", title = "Multivariate second order {Poincar{\'e}} inequalities for {Poisson} functionals", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "130:1--130:42", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573527859", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Zhang:2019:DVK, author = "Xicheng Zhang", title = "A discretized version of {Krylov}'s estimate and its applications", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "131:1--131:17", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573527860", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gerasimovics:2019:HTS, author = "Andris Gerasimovi{\v{c}}s and Martin Hairer", title = "{H{\"o}rmander's} theorem for semilinear {SPDEs}", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "132:1--132:56", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573614084", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Minsker:2019:MIM, author = "Stanislav Minsker and Xiaohan Wei", title = "Moment inequalities for matrix-valued {$U$}-statistics of order 2", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "133:1--133:32", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573614085", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Costantini:2019:MSC, author = "Cristina Costantini and Thomas G. Kurtz", title = "{Markov} selection for constrained martingale problems", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "135:1--135:31", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1573700462", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Beck:2019:SOS, author = "Lisa Beck and Franco Flandoli and Massimiliano Gubinelli and Mario Maurelli", title = "Stochastic {ODEs} and stochastic linear {PDEs} with critical drift: regularity, duality and uniqueness", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "136:1--136:72", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1574996477", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Collevecchio:2019:DWR, author = "Andrea Collevecchio and Kais Hamza and Laurent Tournier", title = "A deterministic walk on the randomly oriented {Manhattan} lattice", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "137:1--137:20", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1575342532", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Baccelli:2019:SGU, author = "Fran{\c{c}}ois Baccelli and Eliza O'Reilly", title = "The stochastic geometry of unconstrained one-bit data compression", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "138:1--138:27", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1575342533", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Benes:2019:TPI, author = "Christian Bene{\v{s}} and Gregory F. Lawler and Fredrik Viklund", title = "Transition probabilities for infinite two-sided loop-erased random walks", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "139:1--139:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1575428689", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Zervos:2019:DSS, author = "Mihail Zervos and Neofytos Rodosthenous and Pui Chan Lon and Thomas Bernhardt", title = "Discretionary stopping of stochastic differential equations with generalised drift", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "140:1--140:39", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1575514915", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ren:2019:SCL, author = "Yan-Xia Ren and Renming Song and Zhenyao Sun and Jianjie Zhao", title = "Stable central limit theorems for super {Ornstein--Uhlenbeck} processes", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "141:1--141:42", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1576638110", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fontes:2019:ABA, author = "Luiz Renato Fontes and V{\'e}ronique Gayrard", title = "Asymptotic behavior and aging of a low temperature cascading $2$-{GREM} dynamics at extreme time scales", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "142:1--142:50", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1576638111", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Erignoux:2019:EFD, author = "Cl{\'e}ment Erignoux and Marielle Simon", title = "Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "143:1--143:52", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1576810975", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Baverez:2019:MBA, author = "Guillaume Baverez", title = "Modular bootstrap agrees with the path integral in the large moduli limit", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "144:1--144:22", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1576810976", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Barhoumi-Andreani:2019:BFN, author = "Yacine Barhoumi-Andr{\'e}ani and Christoph Koch and Hong Liu", title = "Bivariate fluctuations for the number of arithmetic progressions in random sets", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "145:1--145:32", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1577502322", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Barnes:2019:BMR, author = "Clayton Barnes and Krzysztof Burdzy and Carl-Erik Gauthier", title = "Billiards with {Markovian} reflection laws", journal = j-ELECTRON-J-PROBAB, volume = "24", number = "??", pages = "147:1--147:32", month = "????", year = "2019", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1577761457", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Liu:2020:PIQ, DOI = "https://doi.org/10.1214/19-EJP403", author = "Yuan Liu", title = "The {Poincar{\'e}} inequality and quadratic transportation-variance inequalities", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1:1--1:16", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1578020644", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bellingeri:2020:ITF, DOI = "https://doi.org/10.1214/19-EJP404", author = "Carlo Bellingeri", title = "An {It{\^o}} type formula for the additive stochastic heat equation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "2:1--2:52", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1578366206", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Englander:2020:CTW, DOI = "https://doi.org/10.1214/19-EJP406", author = "J{\'a}nos Engl{\"a}nder and Stanislav Volkov and Zhenhua Wang", title = "The coin-turning walk and its scaling limit", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "3:1--3:38", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1578452592", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Durrett:2020:SCP, DOI = "https://doi.org/10.1214/19-EJP402", author = "Rick Durrett and Dong Yao", title = "The symbiotic contact process", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "4:1--4:21", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1579143695", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Su:2020:PSH, DOI = "https://doi.org/10.1214/20-EJP415", author = "Weicong Su", title = "On the peaks of a stochastic heat equation on a sphere with a large radius", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "5:1--5:38", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1579835021", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Miclo:2020:CMV, DOI = "https://doi.org/10.1214/20-EJP419", author = "Laurent Miclo", title = "On the construction of measure-valued dual processes", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "6:1--6:64", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580202285", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Shen:2020:EID, DOI = "https://doi.org/10.1214/20-EJP411", author = "Yandi Shen and Fang Han and Daniela Witten", title = "Exponential inequalities for dependent {$V$}-statistics via random {Fourier} features", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "7:1--7:18", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580267007", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Spinka:2020:FCS, DOI = "https://doi.org/10.1214/20-EJP420", author = "Yinon Spinka", title = "Finitary coding for the sub-critical {Ising} model with finite expected coding volume", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "8:1--8:27", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580267008", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Perlman:2020:RPS, DOI = "https://doi.org/10.1214/20-EJP418", author = "Michael D. Perlman", title = "Are random permutations spherically uniform?", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "9:1--9:26", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580267009", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kumar:2020:SCP, DOI = "https://doi.org/10.1214/19-EJP407", author = "Umesh Kumar and Markus Riedle", title = "The stochastic {Cauchy} problem driven by a cylindrical {L{\'e}vy} process", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "10:1--10:26", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580267010", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Archer:2020:ISL, DOI = "https://doi.org/10.1214/20-EJP413", author = "Eleanor Archer", title = "Infinite stable looptrees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "11:1--11:48", month = "????", year = "2020", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580267011", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Berthet:2020:ERC, author = "Philippe Berthet and Jean Claude Fort", title = "Exact rate of convergence of the expected", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--16", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/19-EJP410", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Exact-rate-of-convergence-of-the-expected-W_2-distance-between/10.1214/19-EJP410.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gaussian empirical", } @Article{Amir:2020:PMD, author = "Gideon Amir and Rangel Baldasso", title = "Percolation in majority dynamics", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "13:1--13:18", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP414", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580374825", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Guionnet:2020:LDL, author = "Alice Guionnet and Myl{\`e}ne Ma{\"\i}da", title = "Large deviations for the largest eigenvalue of the sum of two random matrices", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "14:1--14:24", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/19-EJP405", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580871680", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Barrera:2020:CPO, author = "Gerardo Barrera and Juan Carlos Pardo", title = "Cut-off phenomenon for {Ornstein--Uhlenbeck} processes driven by {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "15:1--15:33", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP417", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580871681", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Kuhn:2020:EMS, author = "Franziska K{\"u}hn", title = "Existence of ({Markovian}) solutions to martingale problems associated with {L{\'e}vy}-type operators", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "16:1--16:26", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP424", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580871682", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Moinat:2020:LBS, author = "Augustin Moinat and Hendrik Weber", title = "Local bounds for stochastic reaction diffusion equations", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "17:1--17:26", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/19-EJP397", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580871683", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Tran:2020:STS, author = "Huy Tran and Yizheng Yuan", title = "A support theorem for {SLE} curves", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "18:1--18:18", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP425", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580958251", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Wang:2020:FIW, author = "Feng-Yu Wang", title = "Functional inequalities for weighted Gamma distribution on the space of finite measures", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "19:1--19:27", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP426", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580958255", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fradelizi:2020:CIC, author = "Matthieu Fradelizi and Jiange Li and Mokshay Madiman", title = "Concentration of information content for convex measures", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "20:1--20:22", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP416", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1580979618", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bailleul:2020:SMF, author = "Isma{\"e}l Bailleul and R{\'e}mi Catellier and Fran{\c{c}}ois Delarue", title = "Solving mean field rough differential equations", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "21:1--21:51", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/19-EJP409", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1581044444", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Klochkov:2020:UHW, author = "Yegor Klochkov and Nikita Zhivotovskiy", title = "Uniform {Hanson-Wright} type concentration inequalities for unbounded entries via the entropy method", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "22:1--22:30", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP422", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1581130826", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Mourrat:2020:EPF, author = "Jean-Christophe Mourrat and Dmitry Panchenko", title = "Extending the {Parisi} formula along a {Hamilton--Jacobi} equation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "23:1--23:17", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP432", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1581735875", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Drapeau:2020:CFC, author = "Samuel Drapeau and Peng Luo and Dewen Xiong", title = "Characterization of fully coupled {FBSDE} in terms of portfolio optimization", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "24:1--24:26", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP412", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1581735876", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pardoux:2020:MDE, author = "Etienne Pardoux", title = "Moderate deviations and extinction of an epidemic", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "25:1--25:27", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP428", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1581994992", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Banerjee:2020:NAL, author = "Sayan Banerjee and Amarjit Budhiraja and Michael Perlmutter", title = "A new approach to large deviations for the {Ginzburg--Landau} model", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "26:1--26:51", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP434", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1582254382", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Blath:2020:SBC, author = "Jochen Blath and Adri{\'a}n Gonz{\'a}lez Casanova and Noemi Kurt and Maite Wilke-Berenguer", title = "The seed bank coalescent with simultaneous switching", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "27:1--27:21", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/19-EJP401", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1582254383", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ko:2020:FEM, author = "Justin Ko", title = "Free energy of multiple systems of spherical spin glasses with constrained overlaps", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "28:1--28:34", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP431", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1582254384", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hammond:2020:MCP, author = "Alan Hammond and Sourav Sarkar", title = "Modulus of continuity for polymer fluctuations and weight profiles in {Poissonian} last passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "29:1--29:38", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP430", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1582534894", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Berger:2020:SLS, author = "Quentin Berger and Michele Salvi", title = "Scaling limit of sub-ballistic {$1$D} random walk among biased conductances: a story of wells and walls", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "30:1--30:43", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP427", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1582534895", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Basse-OConnor:2020:BET, author = "Andreas Basse-O'Connor and Mark Podolskij and Christoph Th{\"a}le", title = "A {Berry--Esse{\'e}n} theorem for partial sums of functionals of heavy-tailed moving averages", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "31:1--31:31", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP435", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1582858935", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Jego:2020:TPR, author = "Antoine Jego", title = "Thick points of random walk and the {Gaussian} free field", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "32:1--32:39", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP433", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1582858936", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Orenshtein:2020:RWR, author = "Tal Orenshtein and Christophe Sabot", title = "Random walks in random hypergeometric environment", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "33:1--33:21", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP429", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1583805862", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Nilssen:2020:RLP, author = "Torstein Nilssen", title = "Rough linear {PDE's} with discontinuous coefficients --- existence of solutions via regularization by fractional {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "34:1--34:33", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP437", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1584669820", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dareiotis:2020:NDE, author = "Konstantinos Dareiotis and Benjamin Gess", title = "Nonlinear diffusion equations with nonlinear gradient noise", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "35:1--35:43", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP436", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585101794", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fonseca-Mora:2020:SDN, author = "Christian A. Fonseca-Mora", title = "Semimartingales on duals of nuclear spaces", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "36:1--36:24", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP444", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585188065", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Behme:2020:EFM, author = "Anita Behme and Apostolos Sideris", title = "Exponential functionals of {Markov} additive processes", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "37:1--37:25", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP441", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585274716", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Le:2020:SSL, author = "Khoa L{\^e}", title = "A stochastic sewing lemma and applications", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "38:1--38:55", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP442", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585620093", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Perruchaud:2020:HAK, author = "Pierre Perruchaud", title = "Homogenisation for anisotropic kinetic random motions", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "39:1--39:26", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP439", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585620094", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dalang:2020:OLB, author = "Robert C. Dalang and Fei Pu", title = "Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--31", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP438", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60J45; 60H07; 60G60", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Optimal-lower-bounds-on-hitting-probabilities-for-stochastic-heat-equations/10.1214/20-EJP438.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "hitting probabilities; Malliavin calculus; spatially homogeneous Gaussian noise; systems of non-linear stochastic heat equations", } @Article{Kopytko:2020:ODD, author = "Bohdan Kopytko and Roman Shevchuk", title = "One-dimensional diffusion processes with moving membrane: partial reflection in combination with jump-like exit of process from membrane", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "41:1--41:21", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP443", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585620096", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Procaccia:2020:SDW, author = "Eviatar B. Procaccia and Ron Rosenthal and Yuan Zhang", title = "Stabilization of {DLA} in a wedge", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "42:1--42:22", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP446", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585879250", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Martin:2020:SDM, author = "James B. Martin", title = "Stationary distributions of the multi-type {ASEP}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "43:1--43:41", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP421", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585879251", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Albeverio:2020:WSS, author = "Sergio Albeverio and Francesco C. {De Vecchi} and Paola Morando and Stefania Ugolini", title = "Weak symmetries of stochastic differential equations driven by semimartingales with jumps", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "44:1--44:34", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP440", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1585965704", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hansen:2020:EUQ, author = "Mads Christian Hansen and Wiuf Carsten", title = "Existence of a unique quasi-stationary distribution in stochastic reaction networks", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "45:1--45:30", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP445", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1587024023", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Dupuis:2020:LDC, author = "Paul Dupuis and Vaios Laschos and Kavita Ramanan", title = "Large deviations for configurations generated by {Gibbs} distributions with energy functionals consisting of singular interaction and weakly confining potentials", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "46:1--46:41", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP449", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1587693777", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bhamidi:2020:UCH, author = "Shankar Bhamidi and Souvik Dhara and Remco van der Hofstad and Sanchayan Sen", title = "Universality for critical heavy-tailed network models: Metric structure of maximal components", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "47:1--47:57", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/19-EJP408", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1587693778", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Nualart:2020:AGF, author = "David Nualart and Guangqu Zheng", title = "Averaging {Gaussian} functionals", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "48:1--48:54", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP453", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588039467", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Michelen:2020:FMN, author = "Marcus Michelen and Josh Rosenberg", title = "The frog model on non-amenable trees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "49:1--49:16", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP454", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588039468", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Wong:2020:SPI, author = "Chi Hong Wong and Xue Yang and Jing Zhang", title = "Stochastic partial integral-differential equations with divergence terms", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "50:1--50:22", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP448", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588039469", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Maller:2020:CCP, author = "Ross A. Maller and David M. Mason", title = "Compactness and continuity properties for a {L{\'e}vy} process at a two-sided exit time", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "51:1--51:26", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP451", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588125886", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Popov:2020:TCW, author = "Serguei Popov and Leonardo T. Rolla and Daniel Ungaretti", title = "Transience of conditioned walks on the plane: encounters and speed of escape", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "52:1--52:23", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP458", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588125887", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Penrose:2020:LLP, author = "Mathew D. Penrose", title = "Leaves on the line and in the plane", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "53:1--53:40", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP447", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588644036", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Forsstrom:2020:DCR, author = "Malin P. Forsstr{\"o}m and Jeffrey E. Steif", title = "Divide and color representations for threshold {Gaussian} and stable vectors", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "54:1--54:45", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP459", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588644037", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Pekoz:2020:ELA, author = "Erol A. Pek{\"o}z and Adrian R{\"o}llin and Nathan Ross", title = "Exponential and {Laplace} approximation for occupation statistics of branching random walk", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "55:1--55:22", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP461", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588644038", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Foutel-Rodier:2020:KCE, author = "F{\'e}lix Foutel-Rodier and Amaury Lambert and Emmanuel Schertzer", title = "{Kingman}'s coalescent with erosion", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "56:1--56:33", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP450", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588644039", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Cox:2020:RSL, author = "J. Theodore Cox and Edwin A. Perkins", title = "Rescaling the spatial {Lambda--Fleming--Viot} process and convergence to super-{Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "57:1--57:56", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP452", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588644040", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Fatkullin:2020:HLY, author = "Ibrahim Fatkullin and Sunder Sethuraman and Jianfei Xue", title = "On hydrodynamic limits of {Young} diagrams", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "58:1--58:44", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP455", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588644041", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Najnudel:2020:CVR, author = "Joseph Najnudel", title = "On consecutive values of random completely multiplicative functions", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "59:1--59:28", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP456", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588644042", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Maffucci:2020:RAL, author = "Riccardo W. Maffucci", title = "Restriction of {$3$D} arithmetic {Laplace} eigenfunctions to a plane", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "60:1--60:17", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP457", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1588924817", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Mach:2020:RTP, author = "Tibor Mach and Anja Sturm and Jan M. Swart", title = "Recursive tree processes and the mean-field limit of stochastic flows", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "61:1--61:63", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP460", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1589335470", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Panloup:2020:SEC, author = "Fabien Panloup and Alexandre Richard", title = "Sub-exponential convergence to equilibrium for {Gaussian} driven Stochastic Differential Equations with semi-contractive drift", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "62:1--62:43", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP464", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1591084854", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Mijatovic:2020:SOZ, author = "Aleksandar Mijatovi{\'c} and Vladislav Vysotsky", title = "Stability of overshoots of zero mean random walks", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "63:1--63:22", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP463", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1591668284", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Thevenin:2020:VFO, author = "Paul Th{\'e}venin", title = "Vertices with fixed outdegrees in large {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "64:1--64:25", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP465", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1592445678", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Abacherli:2020:LSPa, author = "Angelo Ab{\"a}cherli and Ji{\v{r}}{\'\i} {\v{C}}ern{\'y}", title = "Level-set percolation of the {Gaussian} free field on regular graphs {I}: regular trees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "65:1--65:24", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP468", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1592445679", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Corwin:2020:KET, author = "Ivan Corwin and Promit Ghosal", title = "{KPZ} equation tails for general initial data", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "66:1--66:38", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP467", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1592618468", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Borga:2020:DTA, author = "Jacopo Borga and Mathilde Bouvel and Valentin F{\'e}ray and Benedikt Stufler", title = "A decorated tree approach to random permutations in substitution-closed classes", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "67:1--67:52", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP469", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1592618469", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Freeman:2020:ECM, author = "Nic Freeman and Jonathan Jordan", title = "Extensive condensation in a model of preferential attachment with fitness", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "68:1--68:42", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP462", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1592964036", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Grotto:2020:SSD, author = "Francesco Grotto", title = "Stationary solutions of damped stochastic $2$-dimensional {Euler}'s equation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "69:1--69:24", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP474", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1593137129", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Hora:2020:EMP, author = "Akihito Hora", title = "Effect of microscopic pausing time distributions on the dynamical limit shapes for random {Young} diagrams", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "70:1--70:21", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP466", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1593137130", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gantert:2020:STP, author = "Nina Gantert and Dominik Schmid", title = "The speed of the tagged particle in the exclusion process on {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "71:1--71:27", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP477", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1593568835", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Cohen:2020:MDO, author = "Philip Cohen and Fabio Deelan Cunden and Neil O'Connell", title = "Moments of discrete orthogonal polynomial ensembles", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "72:1--72:19", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP472", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1593568836", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Gaudio:2020:ARW, author = "Julia Gaudio and Yury Polyanskiy", title = "Attracting random walks", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "73:1--73:31", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP471", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1593568837", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bally:2020:RLC, author = "Vlad Bally and Lucia Caramellino and Guillaume Poly", title = "Regularization lemmas and convergence in total variation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "74:1--74:20", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP481", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1593828035", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Deuschel:2020:QTE, author = "Jean-Dominique Deuschel and Ryoki Fukushima", title = "Quenched tail estimate for the random walk in random scenery and in random layered conductance {II}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "75:1--75:28", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP478", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1593828036", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Lerouvillois:2020:HLD, author = "Vincent Lerouvillois", title = "Hydrodynamic limit of a $ (2 + 1)$-dimensional crystal growth model in the anisotropic {KPZ} class", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--35", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP473", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J25; 60K35; 82C24", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Hydrodynamic-limit-of-a-21-dimensional-crystal-growth-model-in/10.1214/20-EJP473.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "anisotropic KPZ; Hydrodynamic limit; Interface growth", } @Article{Huang:2020:EGC, author = "Xiangying Huang", title = "Exponential growth and continuous phase transitions for the contact process on trees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "77:1--77:21", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP483", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1594432885", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Ferrari:2020:BIM, author = "Pablo A. Ferrari and Davide Gabrielli", title = "{BBS} invariant measures with independent soliton components", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "78:1--78:26", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP475", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1594432886", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Bhattacharjee:2020:CSI, author = "Chinmoy Bhattacharjee and Ilya Molchanov", title = "Convergence to scale-invariant {Poisson} processes and applications in {Dickman} approximation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "79:1--79:20", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP482", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Jul 14 10:14:21 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/euclid.ejp/1594432887", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", } @Article{Linker:2020:CPD, author = "Amitai Linker and Daniel Remenik", title = "The contact process with dynamic edges on {$ \mathbb {Z} $}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--21", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP480", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/The-contact-process-with-dynamic-edges-on-mathbb-Z/10.1214/20-EJP480.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "contact process; Dynamical percolation; random environment", } @Article{Eckhoff:2020:LPF, author = "Maren Eckhoff and Jesse Goodman and Remco van der Hofstad and Francesca R. Nardi", title = "Long paths in first passage percolation on the complete graph {I}. {Local} {PWIT} dynamics", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--45", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP484", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60J80; 60G55", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Long-paths-in-first-passage-percolation-on-the-complete-graph/10.1214/20-EJP484.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "first passage percolation; Invasion percolation; Random graphs", } @Article{Dareiotis:2020:RNE, author = "Konstantinos Dareiotis and M{\'a}t{\'e} Gerencs{\'e}r", title = "On the regularisation of the noise for the {Euler--Maruyama} scheme with irregular drift", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--18", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP479", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H35; 60H10; 65C30", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-the-regularisation-of-the-noise-for-the-Euler--Maruyama/10.1214/20-EJP479.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Euler--Maruyama scheme; quadrature estimates; Stochastic differential equations", } @Article{Karrila:2020:UBM, author = "Alex Karrila", title = "{UST} branches, martingales, and multiple {SLE(2)}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--37", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP485", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B20; 82B27; 60J67; 60G42; 39A12", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/UST-branches-martingales-and-multiple-SLE2/10.1214/20-EJP485.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60Dxx; multiple SLEs; scaling limits; Schramm--Loewner evolutions (SLEs); uniform spanning tree (UST)", } @Article{Xu:2020:HSL, author = "Lu Xu", title = "Hyperbolic scaling limit of non-equilibrium fluctuations for a weakly anharmonic chain", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--40", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP488", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82C05; 82C22", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Hyperbolic-scaling-limit-of-non-equilibrium-fluctuations-for-a-weakly/10.1214/20-EJP488.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Boltzmann--Gibbs principle; hyperbolic scaling limit; non-equilibrium fluctuation; Relative entropy", } @Article{Seppalainen:2020:CEC, author = "Timo Sepp{\"a}l{\"a}inen and Xiao Shen", title = "Coalescence estimates for the corner growth model with exponential weights", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--31", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP489", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See erratum \cite{Seppalainen:2021:ECE}.", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Coalescence-estimates-for-the-corner-growth-model-with-exponential-weights/10.1214/20-EJP489.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "coalescence exit time; fluctuation exponent; Geodesic; Kardar-Parisi-Zhang; Last-passage percolation; random growth model", } @Article{Ishiwata:2020:CLT, author = "Satoshi Ishiwata and Hiroshi Kawabi and Ryuya Namba", title = "Central limit theorems for non-symmetric random walks on nilpotent covering graphs: {Part I}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--46", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP486", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17; 60G50; 60J10; 22E25", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Central-limit-theorems-for-non-symmetric-random-walks-on-nilpotent/10.1214/20-EJP486.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Albanese metric; central limit theorem; discrete geometric analysis; modified harmonic realization; nilpotent covering graph; non-symmetric random walk; rough path theory", } @Article{Lawler:2020:ITS, author = "Gregory F. Lawler", title = "The infinite two-sided loop-erased random walk", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--42", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP476", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/The-infinite-two-sided-loop-erased-random-walk/10.1214/20-EJP476.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "loop measures; Loop-erased random walk", } @Article{Benaim:2020:AAB, author = "Michel Bena{\"\i}m and Charles-Edouard Br{\'e}hier and Pierre Monmarch{\'e}", title = "Analysis of an Adaptive Biasing Force method based on self-interacting dynamics", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--28", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP490", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 65C50", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Analysis-of-an-Adaptive-Biasing-Force-method-based-on-self/10.1214/20-EJP490.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "adaptive biasing; free energy computation; Self-interacting diffusions", } @Article{Chleboun:2020:MSP, author = "Paul Chleboun and Aaron Smith", title = "Mixing of the square plaquette model on a critical length scale", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--53", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP487", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J27; 60J28", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Mixing-of-the-square-plaquette-model-on-a-critical-length/10.1214/20-EJP487.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Glass transition; Markov chain; mixing time; plaquette model; spectral gap", } @Article{Diez:2020:PCM, author = "Antoine Diez", title = "Propagation of chaos and moderate interaction for a piecewise deterministic system of geometrically enriched particles", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--38", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP496", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "35Q70; 60J75; 60J25; 60K35; 82C22", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Propagation-of-chaos-and-moderate-interaction-for-a-piecewise-deterministic/10.1214/20-EJP496.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "58J6; collective motion; jump process; Mean-field limit; run and tumble; Vicsek model", } @Article{Barbour:2020:CMI, author = "A. D. Barbour and Nathan Ross and Yuting Wen", title = "Central moment inequalities using {Stein}'s method", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--21", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP493", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60E15; 60C05", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Central-moment-inequalities-using-Steins-method/10.1214/20-EJP493.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Concentration inequalities; Erd{\H{o}}s--R{\'e}nyi~ random graph; Moment inequalities; Stein's method", } @Article{Fill:2020:PRF, author = "James Allen Fill and Daniel Q. Naiman", title = "The {Pareto} record frontier", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--24", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP492", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 60F05; 60F15; 60G70; 60G17", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/The-Pareto-record-frontier/10.1214/20-EJP492.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "boundary-crossing probabilities; broken records; current records; Extreme value theory; Maxima; Multivariate records; Pareto records; record-setting region; Time change; width of frontier", } @Article{Beliaev:2020:SME, author = "Dmitry Beliaev and Michael McAuley and Stephen Muirhead", title = "Smoothness and monotonicity of the excursion set density of planar {Gaussian} fields", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--37", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP470", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G60; 60G15; 58K05", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Smoothness-and-monotonicity-of-the-excursion-set-density-of-planar/10.1214/20-EJP470.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "critical points; Gaussian fields; Level sets; nodal set", } @Article{Bartl:2020:FIF, author = "Daniel Bartl and Ludovic Tangpi", title = "Functional inequalities for forward and backward diffusions", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--22", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP495", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 60G40; 28C20; 60E15; 60H20; 91G10", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Functional-inequalities-for-forward-and-backward-diffusions/10.1214/20-EJP495.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "backward stochastic differential equation; concentration of measures; logarithmic-Sobolev inequality; non-smooth coefficients; Optimal stopping; quadratic transportation inequality; Stochastic differential equation", } @Article{Kallsen:2020:USM, author = "Jan Kallsen and Paul Kr{\"u}hner", title = "On uniqueness of solutions to martingale problems --- counterexamples and sufficient criteria", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--33", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP494", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "47G30; 60J35; 60J75", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-uniqueness-of-solutions-to-martingale-problems--counterexamples-and/10.1214/20-EJP494.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Jump processes; Markov process; Martingale problem; polynomial process; pseudo-differential operator; symbol; uniqueness", } @Article{Baudoin:2020:RPS, author = "Fabrice Baudoin and Erlend Grong and Kazumasa Kuwada and Robert Neel and Anton Thalmaier", title = "Radial processes for sub-{Riemannian} {Brownian} motions and applications", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--17", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP501", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "53C17; 35H20; 58J65", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Radial-processes-for-sub-Riemannian-Brownian-motions-and-applications/10.1214/20-EJP501.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "H-type group; radial process; Riemannian foliation; Sasakian manifold; stochastic completeness; sub-Laplacian comparison theorem; sub-Riemannian Brownian motion", } @Article{Garban:2020:BFP, author = "Christophe Garban and Hugo Vanneuville", title = "{Bargmann--Fock} percolation is noise sensitive", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--20", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP491", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60G15", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Bargmann--Fock-percolation-is-noise-sensitive/10.1214/20-EJP491.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gaussian fields; Noise sensitivity; percolation; randomized algorithms", } @Article{Lin:2020:SOB, author = "Yiqing Lin and Zhenjie Ren and Nizar Touzi and Junjian Yang", title = "Second order backward {SDE} with random terminal time", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--43", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP498", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10; 60H30", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Second-order-backward-SDE-with-random-terminal-time/10.1214/20-EJP498.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Backward SDE; quasi-sure stochastic analysis; random horizon; second order backward SDE", } @Article{ORourke:2020:LPB, author = "Sean O'Rourke and Noah Williams", title = "On the local pairing behavior of critical points and roots of random polynomials", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--68", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP499", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "30C15; 60F05; 60B10", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-the-local-pairing-behavior-of-critical-points-and-roots/10.1214/20-EJP499.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "critical points; fluctuations of critical points; i.i.d. zeros; Local law; pairing between roots and critical points; random Jordan curves; random polynomials; Wasserstein distance", } @Article{Hutzenthaler:2020:OCD, author = "Martin Hutzenthaler and Arnulf Jentzen and von Wurstemberger Wurstemberger", title = "Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--73", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP423", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H35", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Overcoming-the-curse-of-dimensionality-in-the-approximative-pricing-of/10.1214/20-EJP423.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "curse of dimensionality; high-dimensional PDEs; multilevel~ Picard~ method; semilinear KolmogorovPDEs; Semilinear PDEs", } @Article{Ang:2020:LDR, author = "Morris Ang and Minjae Park and Yilin Wang", title = "Large deviations of radial {SLE}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--13", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP502", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J67; 60F10", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Large-deviations-of-radial-SLE_infty-/10.1214/20-EJP502.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian occupation measure; large deviations; Loewner-Kufarev equation; Schramm-Loewner Evolutions", } @Article{Bell:2020:TRC, author = "James Bell", title = "Time-reversal of coalescing diffusive flows and weak convergence of localized disturbance flows", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--38", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP500", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Time-reversal-of-coalescing-diffusive-flows-and-weak-convergence-of/10.1214/20-EJP500.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Arratia flow; Coalescing flow; disturbance flow; dual flow; stochastic flow; time-reversed flow", } @Article{Stufler:2020:MOS, author = "Benedikt Stufler", title = "On the maximal offspring in a subcritical branching process", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--62", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP506", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60F17; 05C80", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-the-maximal-offspring-in-a-subcritical-branching-process/10.1214/20-EJP506.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "05C0; condensation phenomena; limits of graph parameters; Random trees", } @Article{Alsmeyer:2020:HLC, author = "Gerold Alsmeyer and Zakhar Kabluchko and Alexander Marynych and Vladislav Vysotsky", title = "How long is the convex minorant of a one-dimensional random walk?", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--22", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP497", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60G55; 60J10", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/How-long-is-the-convex-minorant-of-a-one-dimensional/10.1214/20-EJP497.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "convex minorant; random permutation; Random walk", } @Article{Hong:2020:BLT, author = "Jieliang Hong", title = "On the boundary local time measure of super-{Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--66", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP507", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G57; 60J68; 60H30; 35J75; 60J80", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-the-boundary-local-time-measure-of-super-Brownian-motion/10.1214/20-EJP507.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "boundary local time measure; Exit measure; Local time; Super-Brownian motion", } @Article{Azais:2020:NSC, author = "Jean-Marc Aza{\"\i}s and Jos{\'e} R. Le{\'o}n", title = "Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--15", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP508", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G15; 60G60", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Necessary-and-sufficient-conditions-for-the-finiteness-of-the-second/10.1214/20-EJP508.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Kac-Rice formula; Level sets; moments; Random fields", } @Article{Gerard:2020:RVR, author = "Thomas Gerard", title = "Representations of the {Vertex Reinforced Jump Process} as a mixture of {Markov} processes on {$ \mathbb {Z}^d $} and infinite trees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--45", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP510", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J75; 60K37; 31C35", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Representations-of-the-Vertex-Reinforced-Jump-Process-as-a-mixture/10.1214/20-EJP510.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Markov processes in random environment; Martin boundary; Reinforced processes", } @Article{Lun:2020:CSP, author = "Chin Hang Lun and Jon Warren", title = "Continuity and strict positivity of the multi-layer extension of the stochastic heat equation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--41", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP511", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Continuity-and-strict-positivity-of-the-multi-layer-extension-of/10.1214/20-EJP511.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "integrable probability; KPZ equation; Stochastic heat equation", } @Article{Oliveira:2020:IDS, author = "Roberto I. Oliveira and Guilherme H. Reis and Lucas M. Stolerman", title = "Interacting diffusions on sparse graphs: hydrodynamics from local weak limits", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--35", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP505", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F15; 60K35; 60K37; 05C80", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Interacting-diffusions-on-sparse-graphs--hydrodynamics-from-local-weak/10.1214/20-EJP505.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Interacting particle system; local weak limit; Strong law of large numbers", } @Article{Orrieri:2020:LDI, author = "Carlo Orrieri", title = "Large deviations for interacting particle systems: joint mean-field and small-noise limit", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--44", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP516", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Large-deviations-for-interacting-particle-systems--joint-mean-field/10.1214/20-EJP516.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "interacting particle systems; large deviations; stochastic currents", } @Article{Luo:2020:TGS, author = "Peng Luo", title = "A type of globally solvable {BSDEs} with triangularly quadratic generators", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--23", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP504", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10; 60H30", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/A-type-of-globally-solvable-BSDEs-with-triangularly-quadratic-generators/10.1214/20-EJP504.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "BMO martingales; BSDEs; path dependence; triangularly quadratic generators", } @Article{Bisewski:2020:ZLP, author = "Krzysztof Bisewski and Jevgenijs Ivanovs", title = "Zooming-in on a {L{\'e}vy} process: failure to observe threshold exceedance over a dense grid", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--33", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP513", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51; 60F99", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Zooming-in-on-a-L%c3%a9vy-process--failure-to-observe/10.1214/20-EJP513.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "discretization error; high frequency; scaling limits; small-time behavior; supremum", } @Article{Petrov:2020:PIS, author = "Leonid Petrov", title = "{PushTASEP} in inhomogeneous space", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--25", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP517", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82C22; 60C05", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/PushTASEP-in-inhomogeneous-space/10.1214/20-EJP517.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "limit shape; PushTASEP; Schur process; Tracy-Widom distribution", } @Article{Boudabsa:2020:FED, author = "Lotfi Boudabsa and Thomas Simon and Pierre Vallois", title = "Fractional extreme distributions", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--20", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP520", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "26A33; 33E12; 45E10; 60E05; 60G52", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Fractional-extreme-distributions/10.1214/20-EJP520.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "double Gamma function; extreme distribution; fractional differential equation; Kilbas-Saigo function; Le Roy function; stable subordinator", } @Article{FitzGerald:2020:SAF, author = "Will FitzGerald and Roger Tribe and Oleg Zaboronski", title = "Sharp asymptotics for {Fredholm} {Pfaffians} related to interacting particle systems and random matrices", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--15", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP512", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 82C22", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Sharp-asymptotics-for-Fredholm-Pfaffians-related-tointeracting-particle-systems-and/10.1214/20-EJP512.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "annihilating Brownian motions; Ginibre ensemble; Pfaffian point processes; Szego's theorem", } @Article{Talarczyk:2020:LTI, author = "Anna Talarczyk and {\L}ukasz Treszczotko", title = "Limit theorems for integrated trawl processes with symmetric {L{\'e}vy} bases", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--24", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP509", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51; 60F17; 60F05; 60G52; 60G18; 60G57", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Limit-theorems-for-integrated-trawl-processes-with-symmetric-L%c3%a9vy-bases/10.1214/20-EJP509.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "fractional Brownian motion; Infinite divisibility; limit theorems; L{\'e}vy bases; L{\'e}vy processes; Self-similar processes; Stable processes; Trawl processes", } @Article{Caraceni:2020:PUB, author = "Alessandra Caraceni", title = "A polynomial upper bound for the mixing time of edge rotations on planar maps", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--30", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP519", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/A-polynomial-upper-bound-for-the-mixing-time-of-edge/10.1214/20-EJP519.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "edge flips; edge rotations; Markov chain; mixing time; planar maps", } @Article{Barraquand:2020:LDS, author = "Guillaume Barraquand and Mark Rychnovsky", title = "Large deviations for sticky {Brownian} motions", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--52", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP515", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 60F10; 82B23; 82B21; 82C22", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Large-deviations-for-sticky-Brownian-motions/10.1214/20-EJP515.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bethe ansatz; continuum models; interacting particle systems; large deviations; random matrices", } @Article{Etheridge:2020:RLS, author = "Alison M. Etheridge and Amandine V{\'e}ber and Feng Yu", title = "Rescaling limits of the spatial {Lambda-Fleming-Viot} process with selection", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--89", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP523", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G57; 60J25; 92D10; 60J75; 60G52", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Rescaling-limits-of-the-spatial-Lambda-Fleming-Viot-process-with/10.1214/20-EJP523.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Duality; Generalised Fleming-Viot process; limit theorems; natural selection; population genetics; Symmetric stable processes", } @Article{Ferre:2020:LDE, author = "Gr{\'e}goire Ferr{\'e} and Gabriel Stoltz", title = "Large deviations of empirical measures of diffusions in weighted topologies", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--52", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP514", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F10; 60J60; 47D08; 82B31; 82C31", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Large-deviations-of-empirical-measures-of-diffusions-in-weighted-topologies/10.1214/20-EJP514.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Diffusion processes; empirical measures; Feynman--Kac; large deviations; Lyapunov function", } @Article{Huang:2020:ASK, author = "Jingyu Huang and Davar Khoshnevisan", title = "Analysis of a stratified {Kraichnan} flow", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--67", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP524", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 28A80; 35R60; 60K37", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Analysis-of-a-stratified-Kraichnan-flow/10.1214/20-EJP524.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Kraichnan model; macroscopic multifractals; passive scalar transport; Stochastic partial differential equations", } @Article{Buraczewski:2020:ILN, author = "Dariusz Buraczewski and Bohdan Dovgay and Alexander Iksanov", title = "On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking {I}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--24", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP534", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60J80; 60C05", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-intermediate-levels-of-nested-occupancy-scheme-in-random-environment/10.1214/20-EJP534.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bernoulli sieve; GEM distribution; infinite occupancy; random environment; weak convergence; weighted branching process", } @Article{Kendall:2020:RRF, author = "Wilfrid S. Kendall", title = "{Rayleigh} Random Flights on the {Poisson} line {SIRSN}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--36", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP526", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 60G50; 37A50", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Rayleigh-Random-Flights-on-the-Poisson-line-SIRSN/10.1214/20-EJP526.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "abstract scattering representation; critical SIRSN-RRF; Crofton cell; delineated scattering process; Dirichlet forms; dynamical detailed balance; environment viewed from particle; ergodic theorem; fibre process; Kesten-Spitzer-Whitman range theorem; Mecke-Slivnyak theorem; Metropolis--Hastings acceptance ratio; neighbourhood recurrence; Palm conditioning; Poisson line process; RRF (Rayleigh Random Flight); RWRE (Random Walk in a Random Environment); SIRSN (Scale-invariant random spatial network); SIRSN-RRF", } @Article{Li:2020:EEG, author = "Pei-Sen Li and Jian Wang", title = "Exponential ergodicity for general continuous-state nonlinear branching processes", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--25", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP528", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51; 60G52; 60J25; 60J75", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Exponential-ergodicity-for-general-continuous-state-nonlinear-branching-processes/10.1214/20-EJP528.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "continuous-state nonlinear branching process; coupling; exponential ergodicity; strong ergodicity", } @Article{Hebbar:2020:ABB, author = "Pratima Hebbar and Leonid Koralov and James Nolen", title = "Asymptotic behavior of branching diffusion processes in periodic media", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--40", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP527", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60J60; 35K10", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Asymptotic-behavior-of-branching-diffusion-processes-in-periodic-media/10.1214/20-EJP527.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Branching diffusions; Intermittency; large deviations; parabolic PDEs", } @Article{Hutchcroft:2020:BCN, author = "Tom Hutchcroft", title = "The {$ L^2 $} boundedness condition in nonamenable percolation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--27", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP525", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60B99", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/The-L2-boundedness-condition-in-nonamenable-percolation/10.1214/20-EJP525.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Critical exponents; nonamenable; percolation", } @Article{Baci:2020:CIF, author = "Anastas Baci and Carina Betken and Anna Gusakova and Christoph Th{\"a}le", title = "Concentration inequalities for functionals of {Poisson} cylinder processes", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--27", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP529", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 60F10; 52A22; 60E15", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Concentration-inequalities-for-functionals-of-Poisson-cylinder-processes/10.1214/20-EJP529.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Boolean model; concentration inequality; cylindrical integral geometry; intrinsic volume; Poisson cylinder process; Stochastic geometry", } @Article{Mountford:2020:CSA, author = "Thomas Mountford and Maria Eul{\'a}lia Vares and Hao Xue", title = "Critical scaling for an anisotropic percolation system on", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--44", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP533", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60K35", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Critical-scaling-for-an-anisotropic-percolation-system-on-Z-2/10.1214/20-EJP533.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Branching random walk; critical scaling; percolation; renormalization argument", } @Article{Abacherli:2020:LSPb, author = "Angelo Ab{\"a}cherli and Ji{\v{r}}{\'\i} {\v{C}}ern{\'y}", title = "Level-set percolation of the {Gaussian} free field on regular graphs {II}: finite expanders", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--39", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP532", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60G15; 05C48", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Level-set-percolation-of-the-Gaussian-free-field-on-regular/10.1214/20-EJP532.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Expander graphs; Gaussian free field; Level-set percolation; regular graphs", } @Article{Forman:2020:EHM, author = "Noah Forman", title = "Exchangeable hierarchies and mass-structure of weighted real trees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--28", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP522", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B05; 60G09; 60C05", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Exchangeable-hierarchies-and-mass-structure-of-weighted-real-trees/10.1214/20-EJP522.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Continuum random tree; exchangeability; Hierarchy; interval partition; real tree", } @Article{Chen:2020:SMI, author = "Louis H. Y. Chen and Larry Goldstein and Adrian R{\"o}llin", title = "{Stein}'s method via induction", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--49", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP535", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 05C07; 05C80; 05E10", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Steins-method-via-induction/10.1214/20-EJP535.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Erd{\H{o}}s-R{\'e}nyi random graph; Jack measure; Kolmogorov distance; Optimal rates; Stein's method", } @Article{Forman:2020:DSI, author = "Noah Forman and Soumik Pal and Douglas Rizzolo and Matthias Winkel", title = "Diffusions on a space of interval partitions: construction from marked {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--46", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP521", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J25; 60J60; 60J80; 60G18; 60G52; 60G55", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Diffusions-on-a-space-of-interval-partitions--construction-from/10.1214/20-EJP521.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Aldous diffusion; branching processes; Excursion theory; infinitely-many-neutral-alleles model; interval partition; Ray-Knight theorem; self-similar diffusion", } @Article{Kraaij:2020:ERM, author = "Richard C. Kraaij", title = "The exponential resolvent of a {Markov} process and large deviations for {Markov} processes via {Hamilton--Jacobi} equations", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--39", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP539", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F10; 47H20; 60J25; 60J35; 49L25", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/The-exponential-resolvent-of-a-Markov-process-and-large-deviations/10.1214/20-EJP539.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Hamilton--Jacobi equations; large deviations; Markov processes; non-linear resolvent", } @Article{Albenque:2020:SLT, author = "Marie Albenque and Nina Holden and Xin Sun", title = "Scaling limit of triangulations of polygons", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--43", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP537", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 60F17; 05C80", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Scaling-limit-of-triangulations-of-polygons/10.1214/20-EJP537.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian disk; Gromov-Hausdorff-Prokhorov-uniform topology; Scaling limit; Triangulation", } @Article{Jourdain:2020:NFO, author = "B. Jourdain and W. Margheriti", title = "A new family of one dimensional martingale couplings", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--50", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP543", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G42; 60E15; 91G80", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/A-new-family-of-one-dimensional-martingale-couplings/10.1214/20-EJP543.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Convex order; martingale couplings; Martingale optimal transport; Wasserstein distance", } @Article{Chen:2020:HRG, author = "Zhen-Qing Chen and Zimo Hao and Xicheng Zhang", title = "{H{\"o}lder} regularity and gradient estimates for {SDEs} driven by cylindrical", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--23", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP542", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10; 60G52", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/H%c3%b6lder-regularity-and-gradient-estimates-for-SDEs-driven-by-cylindrical/10.1214/20-EJP542.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "H{\"o}lder regularity; Gradient estimate; Littlewood--Paley's decomposition; heat kernel; cylindrical L{\'e}vy process", } @Article{Redig:2020:SSE, author = "Frank Redig and Ellen Saada and Federico Sau", title = "Symmetric simple exclusion process in dynamic environment: hydrodynamics", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--47", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP536", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37; 60J28; 60F17; 82C22", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Symmetric-simple-exclusion-process-in-dynamic-environment-hydrodynamics/10.1214/20-EJP536.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "arbitrary starting point invariance principle; dynamic random conductances; Hydrodynamic limit; symmetric simple exclusion process; tightness criterion", } @Article{Kim:2020:RDP, author = "Daehong Kim and Seiichiro Kusuoka", title = "Recurrence of direct products of diffusion processes in random media having zero potentials", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--18", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP540", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60J60; 60G60; 31C25", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Recurrence-of-direct-products-of-diffusion-processes-in-random-media/10.1214/20-EJP540.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "direct products of diffusion processes; Dirichlet forms; random environment; recurrence", } @Article{Chen:2020:SCS, author = "Le Chen and Kunwoo Kim", title = "Stochastic comparisons for stochastic heat equation", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--38", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP541", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60G60; 35R60", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Stochastic-comparisons-for-stochastic-heat-equation/10.1214/20-EJP541.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "infinite dimensional SDE; moment comparison principle; Parabolic Anderson model; rough initial data; Slepian's inequality for SPDEs; spatially homogeneous noise; stochastic comparison principle; Stochastic heat equation", } @Article{Fountoulakis:2020:LTI, author = "Nikolaos Fountoulakis and Joseph Yukich", title = "Limit theory for isolated and extreme points in hyperbolic random geometric graphs", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--51", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP531", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C80; 05C12; 05C82", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Limit-theory-for-isolated-and-extreme-points-in-hyperbolic-random/10.1214/20-EJP531.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; complex networks; hyperbolic plane; Random geometric graphs", } @Article{Bakhtin:2020:LDP, author = "Yuri Bakhtin and Donghyun Seo", title = "Localization of directed polymers in continuous space", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--56", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP530", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 82B26; 82B44; 82D60; 60E05", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Localization-of-directed-polymers-in-continuous-space/10.1214/20-EJP530.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Directed polymers; Localization; Mukherjee-Varadhan topology; phase transition", } @Article{Driver:2020:OBR, author = "David P. Driver and Michael R. Tehranchi", title = "Optimisation-based representations for branching processes", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--15", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP548", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 93E20; 35B40", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Optimisation-based-representations-for-branching-processes/10.1214/20-EJP548.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "branching process; FKPP equation; front propagation; Stochastic control", } @Article{Adamczak:2020:ASC, author = "Rados{\l}aw Adamczak", title = "On almost sure convergence of random variables with finite chaos decomposition", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--28", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP538", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F99; 60H05; 60B11", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-almost-sure-convergence-of-random-variables-with-finite-chaos/10.1214/20-EJP538.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "multiple stochastic (Wiener-It{\^o}) integrals; Poisson process; polynomial chaos; random multi-linear forms", } @Article{Procaccia:2020:CMP, author = "Eviatar B. Procaccia and Yuan Zhang", title = "On covering monotonic paths with simple random walk", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--39", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP545", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05; 60G50", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-covering-monotonic-paths-with-simple-random-walk/10.1214/20-EJP545.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "covering; monotonic paths; Random walk", } @Article{Lodewijks:2020:PTP, author = "Bas Lodewijks and Marcel Ortgiese", title = "A phase transition for preferential attachment models with additive fitness", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--54", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP550", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C80; 60G42", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/A-phase-transition-for-preferential-attachment-models-with-additive-fitness/10.1214/20-EJP550.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "additive fitness; maximum degree; network models; Preferential attachment model; scale-free property", } @Article{Herman:2020:STC, author = "John Herman and Ifan Johnston and Lorenzo Toniazzi", title = "Space-time coupled evolution equations and their stochastic solutions", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--21", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP544", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "35R11; 45K05; 35C15; 60H30", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Space-time-coupled-evolution-equations-and-their-stochastic-solutions/10.1214/20-EJP544.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "exterior boundary conditions; Feller semigroup; space-time coupled evolution equation; Subordination", } @Article{Lin:2020:STE, author = "Yier Lin", title = "The stochastic telegraph equation limit of the stochastic higher spin six vertex model", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--30", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP552", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 82B20", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/The-stochastic-telegraph-equation-limit-of-the-stochastic-higher-spin/10.1214/20-EJP552.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "functional central limit theorem; Fusion; stochastic higher spin six vertex model; stochastic telegraph equation", } @Article{Herry:2020:SLT, author = "Ronan Herry", title = "Stable limit theorems on the {Poisson} space", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--30", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP557", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60G55; 60H05; 60H07; 60E10", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Stable-limit-theorems-on-the-Poisson-space/10.1214/20-EJP557.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "limit theorems; Malliavin-Stein; Poisson point process; stable convergence", } @Article{Bourguin:2020:AHV, author = "Solesne Bourguin and Simon Campese", title = "Approximation of {Hilbert}-Valued {Gaussians} on {Dirichlet} structures", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--30", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP551", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "46N30; 60B12; 60F17; 46G12", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Approximation-of-Hilbert-Valued-Gaussians-on-Dirichlet-structures/10.1214/20-EJP551.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Dirichlet structures; fourth moment conditions; Functional limit theorems; Gaussian approximation; Gaussian measures on Hilbert spaces; probabilistic metrics; Stein's method on Banach spaces", } @Article{Zhang:2020:LDS, author = "Rangrang Zhang", title = "Large deviations for stochastic porous media equations", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--42", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP556", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F10; 60H15; 35R60", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Large-deviations-for-stochastic-porous-media-equations/10.1214/20-EJP556.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Kinetic solution; large deviations; porous media equations; weak convergence approach", } @Article{Muller:2020:TFG, author = "Sebastian M{\"u}ller and Gundelinde Maria Wiegel", title = "On transience of frogs on {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--30", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP558", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60J10; 60J85", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/On-transience-of-frogs-on-GaltonWatson-trees/10.1214/20-EJP558.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "branching Markov chain; frog model; Recurrence and transience", } @Article{Uchiyama:2020:PFL, author = "Kohei Uchiyama", title = "The potential function and ladder heights of a recurrent random walk on {$ \mathbb {Z} $} with infinite variance", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--24", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP553", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 60J45", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/The-potential-function-and-ladder-heights-of-a-recurrent-random/10.1214/20-EJP553.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "First hitting time; infinite variance; ladder height; potential function; recurrent random walk", } @Article{Asselah:2020:DCR, author = "Amine Asselah and Bruno Schapira", title = "Deviations for the capacity of the range of a random walk", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--28", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP560", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60G50", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Deviations-for-the-capacity-of-the-range-of-a-random/10.1214/20-EJP560.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "capacity; large deviations; Moderate deviations; Random walk; range", } @Article{Bobkov:2020:PIN, author = "S. G. Bobkov and G. P. Chistyakov and F. G{\"o}tze", title = "{Poincar{\'e}} inequalities and normal approximation for weighted sums", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--31", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP549", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Poincar%c3%a9-inequalities-and-normal-approximation-for-weighted-sums/10.1214/20-EJP549.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60E; 60FEJP; central limit theorem; Normal approximation; typical distributions", } @Article{Corwin:2020:SLW, author = "Ivan Corwin and Li-Cheng Tsai", title = "{SPDE} limit of weakly inhomogeneous {ASEP}", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--55", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP565", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82C22", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/SPDE-limit-of-weakly-inhomogeneous-ASEP/10.1214/20-EJP565.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "inhomogeneous enviornments; interacting particle systems; Stochastic partial differential equations", } @Article{Arnaudon:2020:DFP, author = "Marc Arnaudon and Pierre {Del Moral}", title = "A duality formula and a particle {Gibbs} sampler for continuous time {Feynman--Kac} measures on path spaces", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--54", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP546", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60H35; 37L05; 47D08", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/A-duality-formula-and-a-particle-Gibbs-sampler-for-continuous/10.1214/20-EJP546.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "ancestral lines; contraction inequalities; Dyson-Phillips expansions; Feynman--Kac formulae; genealogical trees; Gibb-Glauber dynamics; interacting particle systems; propagation of chaos properties", } @Article{Aziznejad:2020:WAB, author = "Shayan Aziznejad and Julien Fageot", title = "Wavelet analysis of the {Besov} regularity of {L{\'e}vy} white noise", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--38", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP554", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51; 46E35; 60G20; 42C40", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Wavelet-analysis-of-the-Besov-regularity-of-L%c3%a9vy-white-noise/10.1214/20-EJP554.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "generalized random processes; L{\'e}vy white noise; moment estimates; Wavelets; weighted Besov spaces", } @Article{Larsson:2020:EPM, author = "Martin Larsson and Sara Svaluto-Ferro", title = "Existence of probability measure valued jump-diffusions in generalized {Wasserstein} spaces", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--25", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP562", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 60J75; 60G57", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Existence-of-probability-measure-valued-jump-diffusions-in-generalized-Wasserstein/10.1214/20-EJP562.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Martingale problem; McKean--Vlasov equations; positive maximum principle; probability measure valued processes; Wasserstein spaces", } @Article{Ang:2020:VMB, author = "Morris Ang and Hugo Falconet and Xin Sun", title = "Volume of metric balls in {Liouville} quantum gravity", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--50", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP564", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Volume-of-metric-balls-in-Liouville-quantum-gravity/10.1214/20-EJP564.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Conformal Structure; Gaussian free field; Liouville Brownian motion; Liouville quantum gravity; metric balls", } @Article{Chaumont:2020:FTS, author = "Lo{\"\i}c Chaumont and Marine Marolleau", title = "Fluctuation theory for spectrally positive additive {L{\'e}vy} fields", journal = j-ELECTRON-J-PROBAB, volume = "25", number = "??", pages = "1--26", month = "", year = "2020", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP547", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51", bibdate = "Tue Mar 30 15:22:58 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Fluctuation-theory-for-spectrally-positive-additive-L%c3%a9vy-fields/10.1214/20-EJP547.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "additive L{\'e}vy field; fluctuation theory; Kemperman's formula; multivariate first hitting time", } @Article{Brown:2021:SCC, author = "Suzie Brown and Paul A. Jenkins and Adam M. Johansen and Jere Koskela", title = "Simple conditions for convergence of sequential {Monte Carlo} genealogies with applications", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--22", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP561", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J90; 60J95; 65C05; 65C35", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Simple-conditions-for-convergence-of-sequential-Monte-Carlo-genealogies-with/10.1214/20-EJP561.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Coalescent; Interacting particle system; particle filter; Resampling; selection", } @Article{Buraczewski:2021:SSS, author = "Dariusz Buraczewski and Konrad Kolesko and Matthias Meiners", title = "Self-similar solutions to kinetic-type evolution equations: beyond the boundary case", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--18", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP568", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 35B40; 60J80; 82C40", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Self-similar-solutions-to-kinetic-type-evolution-equations--beyond/10.1214/20-EJP568.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Branching random walk; Kac model; Kinetic equation; Random trees; smoothing transform", } @Article{Kabluchko:2021:FRG, author = "Zakhar Kabluchko and Christoph Th{\"a}le", title = "Faces in random great hypersphere tessellations", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--35", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP570", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Faces-in-random-great-hypersphere-tessellations/10.1214/20-EJP570.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "great hypersphere tessellation", } @Article{Boenkost:2021:HFC, author = "Florin Boenkost and Adri{\'a}n Gonz{\'a}lez Casanova and Cornelia Pokalyuk and Anton Wakolbinger", title = "{Haldane}'s formula in {Cannings} models: the case of moderately weak selection", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--36", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP572", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10; 60J80; 60F05; 92D15; 92D25", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Haldanes-formula-in-Cannings-models-thecaseofmoderately-weak-selection/10.1214/20-EJP572.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "ancestral selection graph; Cannings model; directional selection; probability of fixation; sampling duality", } @Article{Dassios:2021:EST, author = "Angelos Dassios and Junyi Zhang", title = "Exact simulation of two-parameter {Poisson--Dirichlet} random variables", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--20", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP573", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G57; 60G51; 65C10", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Exact-simulation-of-two-parameter-Poisson--Dirichlet-random-variables/10.1214/20-EJP573.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "exact simulation; subordinator; two-parameter Poisson--Dirichlet distribution", } @Article{Figueiredo:2021:RWG, author = "Daniel Figueiredo and Giulio Iacobelli and Roberto Oliveira and Bruce Reed and Rodrigo Ribeiro", title = "On a random walk that grows its own tree", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--40", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP574", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K35; 60K35", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-a-random-walk-that-grows-its-own-tree/10.1214/20-EJP574.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "dynamic random environments; Local weak convergence; random environments; Random trees; Random walks; transience", } @Article{Lambert:2021:MCL, author = "Gaultier Lambert", title = "Mesoscopic central limit theorem for the circular", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--33", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP559", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Mesoscopic-central-limit-theorem-for-the-circular-beta--ensembles/10.1214/20-EJP559.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "loop equations for", } @Article{Huang:2021:NMC, author = "De Huang and Joel A. Tropp", title = "Nonlinear matrix concentration via semigroup methods", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--31", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP578", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 46N30; 60J25; 46L53", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Nonlinear-matrix-concentration-via-semigroup-methods/10.1214/20-EJP578.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bakry--{\'E}mery criterion; concentration inequality; functional inequality; local Poincar{\'e} inequality; Markov process; matrix concentration; semigroup", } @Article{Oh:2021:CSN, author = "Tadahiro Oh and Mamoru Okamoto", title = "Comparing the stochastic nonlinear wave and heat equations: a case study", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--44", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP575", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "35L71; 35K15; 60H15", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Comparing-the-stochastic-nonlinear-wave-and-heat-equations--a/10.1214/20-EJP575.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Nonlinear heat equation; Nonlinear wave equation; renormalization; stochastic nonlinear heat equation; stochastic nonlinear wave equation; Stochastic quantization equation; White noise", } @Article{Legrand:2021:IDD, author = "Alexandre Legrand", title = "Influence of disorder on {DNA} denaturation: the disordered generalized {Poland--Scheraga} model", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--43", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP563", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82D60; 92C05; 60K05", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Influence-of-disorder-on-DNA-denaturation--thedisordered-generalized-Poland/10.1214/20-EJP563.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Critical behavior; disorder relevance; disordered polymer models; DNA denaturation; shift of the critical point", } @Article{Adamczak:2021:MGC, author = "Rados{\l}aw Adamczak and Rafa{\l} Lata{\l}a and Rafa{\l} Meller", title = "Moments of {Gaussian} chaoses in {Banach} spaces", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--36", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP567", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60E15; 60G15; 60B11", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Moments-of-Gaussian-chaoses-in-Banach-spaces/10.1214/20-EJP567.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gaussian chaoses; Gaussian processes; Metric entropy; polynomials in independent random variables; Tail and moment inequalities", } @Article{Criens:2021:ACS, author = "David Criens", title = "On absolute continuity and singularity of multidimensional diffusions", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--26", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP555", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 60G44; 60H10; 91B70", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-absolute-continuity-and-singularity-of-multidimensional-diffusions/10.1214/20-EJP555.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Absolute continuity; explosion; Integral test; multidimensional diffusion; perpetual integral; Random time change; singularity; uniformly integrable martingale", } @Article{Fountoulakis:2021:CHM, author = "Nikolaos Fountoulakis and Pim van der Hoorn and Tobias M{\"u}ller and Markus Schepers", title = "Clustering in a hyperbolic model of complex networks", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--132", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP583", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C80", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Clustering-in-a-hyperbolic-model-of-complex-networks/10.1214/21-EJP583.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "clustering; hyperbolic random graph; Random graphs", } @Article{Mucha:2021:STO, author = "Jacek Mucha", title = "Spectral theory for one-dimensional (non-symmetric) stable processes killed upon hitting the origin", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--33", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP594", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51; 60G52; 60J35; 60J45", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Spectral-theory-for-one-dimensional-non-symmetric-stable-processes-killed/10.1214/21-EJP594.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "hitting time; Spectral theory; Stable process; Transition density", } @Article{Huang:2021:DED, author = "Xing Huang and Feng-Yu Wang", title = "Derivative estimates on distributions of {McKean--Vlasov} {SDEs}", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--12", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP582", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G44", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Derivative-estimates-on-distributions-of-McKean--Vlasov-SDEs/10.1214/21-EJP582.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60H1075; heat kernel parameter expansion; intrinsic derivative; L-derivative; Mckean-Vlasov SDEs", } @Article{Luh:2021:ECN, author = "Kyle Luh and Sean O'Rourke", title = "Eigenvectors and controllability of non-{Hermitian} random matrices and directed graphs", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--43", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP588", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 93E03", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Eigenvectors-and-controllability-of-non-Hermitian-random-matrices-and-directed/10.1214/21-EJP588.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Controllability; eigenvectors; non-Hermitian; Random matrix", } @Article{Dalang:2021:MPG, author = "Robert C. Dalang and Cheuk Yin Lee and Carl Mueller and Yimin Xiao", title = "Multiple points of {Gaussian} random fields", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--25", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP589", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G15; 60G17; 60G60", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Multiple-points-of-Gaussian-random-fields/10.1214/21-EJP589.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "critical dimension; Fractional Brownian sheet; Gaussian random fields; multiple points; Stochastic heat and wave equations", } @Article{Carrance:2021:CET, author = "Ariane Carrance", title = "Convergence of {Eulerian} triangulations", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--48", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP579", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C80; 60B05; 60J80; 05A16", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Convergence-of-Eulerian-triangulations/10.1214/21-EJP579.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "branching processes; local limits of maps; Random maps; scaling limits of maps", } @Article{Komorowski:2021:HLC, author = "Tomasz Komorowski and Stefano Olla and Marielle Simon", title = "Hydrodynamic limit for a chain with thermal and mechanical boundary forces", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--49", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP581", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82C70; 60K35", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Hydrodynamic-limit-for-a-chain-with-thermal-and-mechanical-boundary/10.1214/21-EJP581.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "boundary conditions; Fourier-Wigner functions; harmonic chain; Hydrodynamic limit", } @Article{Erny:2021:CPC, author = "Xavier Erny and Eva L{\"o}cherbach and Dasha Loukianova", title = "Conditional propagation of chaos for mean field systems of interacting neurons", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--25", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP580", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J76; 60K35; 60G55; 60G09", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Conditional-propagation-of-chaos-for-mean-field-systems-of-interacting/10.1214/21-EJP580.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "empirical measure; exchangeability; Hewitt Savage theorem; interacting particle systems; Martingale problem; mean field interaction; Piecewise deterministic Markov processes; propagation of chaos", } @Article{Osekowski:2021:SMB, author = "Adam Os{\k{e}}kowski and Yahui Zuo", title = "Sharp maximal {$ L^p $}-bounds for continuous martingales and their differential subordinates", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--22", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP596", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G44", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Sharp-maximal-Lp-bounds-for-continuous-martingales-and-their-differential/10.1214/21-EJP596.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Differential subordination; martingale; maximal inequality; stochastic integral", } @Article{Cass:2021:LTB, author = "Thomas Cass and Dan Crisan and Paul Dobson and Michela Ottobre", title = "Long-time behaviour of degenerate diffusions: {UFG}-type {SDEs} and time-inhomogeneous hypoelliptic processes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--72", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP577", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10; 35K10; 35B35; 35B65; 58J65; 49J55; 93E03; 37H10", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Long-time-behaviour-of-degenerate-diffusions--UFG-type-SDEs/10.1214/20-EJP577.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Diffusion Semigroups; parabolic PDE; UFG condition; H{\"o}rmander condition; long time asymptotics; processes with multiple invariant measures; non-ergodic SDEs; distributions with non-constant rank; stochastic control theory", } @Article{Cancrini:2021:PCG, author = "Nicoletta Cancrini and Gustavo Posta", title = "Propagation of chaos for a general balls into bins dynamics", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--20", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP590", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60B10", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Propagation-of-chaos-for-a-general-balls-into-bins-dynamics/10.1214/21-EJP590.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "chaos propagation; Interacting particle system; parallel updates; queues network", } @Article{Cipolloni:2021:FAC, author = "Giorgio Cipolloni and L{\'a}szl{\'o} Erd{\H{o}}s and Dominik Schr{\"o}der", title = "Fluctuation around the circular law for random matrices with real entries", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--61", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP591", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 15B52", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Fluctuation-around-the-circular-law-for-random-matrices-with-real/10.1214/21-EJP591.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; Dyson Brownian motion; Girko's formula; linear statistics; Local law", } @Article{Biswas:2021:SLF, author = "Niloy Biswas and Alison Etheridge and Aleksander Klimek", title = "The spatial {Lambda-Fleming-Viot} process with fluctuating selection", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--51", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP593", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G57; 60J25; 92D15; 60H15; 60G55", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-spatial-Lambda-Fleming-Viot-process-with-fluctuating-selection/10.1214/21-EJP593.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "fluctuating selection; scaling limits; spatial Lambda Fleming-Viot model; Stochastic growth models; tracer dynamics", } @Article{Rivera:2021:TIP, author = "Alejandro Rivera", title = "{Talagrand}'s inequality in planar {Gaussian} field percolation", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--25", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP585", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G60; 60K35; 82B43; 82C43", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Talagrands-inequality-in-planar-Gaussian-field-percolation/10.1214/21-EJP585.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gaussian fields; percolation; phase transition", } @Article{Ayala:2021:HOF, author = "Mario Ayala and Gioia Carinci and Frank Redig", title = "Higher order fluctuation fields and orthogonal duality polynomials", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--35", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP586", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 35K55", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Higher-order-fluctuation-fields-and-orthogonal-duality-polynomials/10.1214/21-EJP586.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "fluctuation fields; higher-order fields; orthogonal polynomials; self-duality", } @Article{Dobler:2021:SME, author = "Christian D{\"o}bler and Miko{\l}aj J. Kasprzak", title = "{Stein}'s method of exchangeable pairs in multivariate functional approximations", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--50", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP587", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B10; 60F17; 60J65; 60E05; 60E15", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Steins-method-of-exchangeable-pairs-in-multivariate-functional-approximations/10.1214/21-EJP587.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "0B12; Exchangeable pairs; Functional convergence; multivariate processes; Stein's method; U-statistics", } @Article{Kalinin:2021:SCR, author = "Alexander Kalinin", title = "Support characterization for regular path-dependent stochastic {Volterra} integral equations", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--29", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP576", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H20; 28C20; 60G17; 45D05; 45J05", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Support-characterization-for-regular-path-dependent-stochastic-Volterra-integral-equations/10.1214/20-EJP576.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "support of a measure; path-dependent Volterra process; functional Volterra integral equation; functional It{\^o} calculus; vertical derivative; H{\"o}lder space", } @Article{Konarovskyi:2021:SBM, author = "Vitalii Konarovskyi and Vlada Limic", title = "Stochastic block model in a new critical regime and the interacting multiplicative coalescent", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--23", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP584", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J75; 60K35; 60B12; 05C80", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Stochastic-block-model-in-a-new-critical-regime-and-the/10.1214/21-EJP584.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "multiplicative coalescent; near-critical; phase transition; random graph; Stochastic block model", } @Article{Aksamit:2021:TTR, author = "Anna Aksamit and Tahir Choulli and Monique Jeanblanc", title = "Thin times and random times' decomposition", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--22", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP569", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G07; 60G40; 60G44", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Thin-times-and-random-times-decomposition/10.1214/20-EJP569.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "(semi)martingale stability; avoidance of stopping time; dual optional projection; graph of a random time; Honest times; hypothesis (H{\prime}); immersion; progressive enlargement of filtration; thin times; thin-thick decomposition", } @Article{Zhan:2021:TCG, author = "Dapeng Zhan", title = "Two-curve {Green}'s function for $2$-{SLE}: the boundary case", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--58", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP592", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Two-curve-Greens-function-for-2-SLE--the-boundary/10.1214/21-EJP592.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "30C; 60G; Green's function; multiple SLE; SLE", } @Article{Emrah:2021:FSC, author = "Elnur Emrah and Christopher Janjigian and Timo Sepp{\"a}l{\"a}inen", title = "Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--45", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP595", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Flats-spikes-and-crevices--the-evolving-shape-of-the/10.1214/21-EJP595.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Corner growth model; flux; Last-passage percolation; Limit shapes; TASEP", } @Article{McKenna:2021:LDE, author = "Benjamin McKenna", title = "Large deviations for extreme eigenvalues of deformed {Wigner} random matrices", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--37", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/20-EJP571", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 60F10", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Large-deviations-for-extreme-eigenvalues-of-deformed-Wigner-random-matrices/10.1214/20-EJP571.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Deformed Wigner matrices; Extreme eigenvalues; large deviations; random matrices", } @Article{Ledger:2021:MCN, author = "Sean Ledger and Andreas S{\o}jmark", title = "At the mercy of the common noise: blow-ups in a conditional {McKean--Vlasov} Problem", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--39", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP597", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G57; 60H15; 60H30; 82C22; 34B16", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/At-the-mercy-of-the-common-noise--blow-ups/10.1214/21-EJP597.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "blow-ups; common noise; contagion; McKean--Vlasov problem; Particle system; weak convergence", } @Article{Chen:2021:UAM, author = "Wei-Kuo Chen and Wai-Kit Lam", title = "Universality of approximate message passing algorithms", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--44", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP604", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 62E20; 68W40", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Universality-of-approximate-message-passing-algorithms/10.1214/21-EJP604.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "message passing; spike recovery; spiked random matrix; Universality", } @Article{Liu:2021:SLC, author = "Mingchang Liu and Hao Wu", title = "Scaling limits of crossing probabilities in metric graph {GFF}", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--46", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP598", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G15; 60G60; 60J67", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Scaling-limits-of-crossing-probabilities-in-metric-graph-GFF/10.1214/21-EJP598.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Crossing probability; Gaussian free field; Schramm Loewner Evolution", } @Article{Baudoin:2021:AWB, author = "Fabrice Baudoin and Jing Wang", title = "Asymptotic windings of the block determinants of a unitary {Brownian} motion and related diffusions", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "??", pages = "1--21", month = "", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP600", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 60B20; 60J35", bibdate = "Tue Mar 30 15:23:09 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Asymptotic-windings-of-the-block-determinants-of-a-unitary-Brownian/10.1214/21-EJP600.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "asymptotic stochastic area; asymptotic windings; block determinants; Brownian motion of complex Grassmannian manifold; Stiefel Brownian motion", } @Article{Dumaz:2021:OLH, author = "Laure Dumaz and Yun Li and Benedek Valk{\'o}", title = "Operator level hard-to-soft transition for $ \beta $-ensembles", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--28", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP602", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 47B80; 47E05", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Operator-level-hard-to-soft-transition-for-%ce%b2-ensembles/10.1214/21-EJP602.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "random differential operators; random matrices", } @Article{Che:2021:ULS, author = "Ziliang Che and Patrick Lopatto", title = "Universality of the least singular value for the sum of random matrices", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--38", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP603", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Universality-of-the-least-singular-value-for-the-sum-of/10.1214/21-EJP603.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Random matrix theory; Singular value; sparse; Universality", } @Article{Benes:2021:RCP, author = "Christian Bene{\v{s}}", title = "Rates of convergence for the planar discrete {Green}'s function in {Pacman} domains", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--14", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP599", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 31A15", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Rates-of-convergence-for-the-planar-discrete-Greens-function-in/10.1214/21-EJP599.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Green's function; rate of convergence; Simple random walk", } @Article{Peretz:2021:MDS, author = "Tal Peretz", title = "Moderate deviations for the self-normalized random walk in random scenery", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--16", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP607", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F10; 60G50; 60K37", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Moderate-deviations-for-the-self-normalized-random-walk-in-random/10.1214/21-EJP607.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Local times; Moderate deviations; Random walk in random scenery; self-normalized partial sums", } @Article{Nestoridi:2021:FSR, author = "Evita Nestoridi and Oanh Nguyen", title = "The full spectrum of random walks on complete finite $d$-ary trees", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--17", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP608", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-full-spectrum-of-random-walks-on-complete-finite-d/10.1214/21-EJP608.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Random walk; regular trees; spectrum", } @Article{Baudoin:2021:TIM, author = "Fabrice Baudoin and Nathaniel Eldredge", title = "Transportation inequalities for {Markov} kernels and their applications", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--30", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP605", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "47D07; 49Q22; 28A33; 58J65", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Transportation-inequalities-for-Markov-kernels-and-their-applications/10.1214/21-EJP605.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "functional inequalities; Hellinger distance; Kantorovich--Wasserstein distance; Kuwada duality; Markov kernels; Optimal transport; reverse logarithmic Sobolev inequality; Reverse Poincar{\'e} inequality", } @Article{Ameur:2021:LTP, author = "Yacin Ameur", title = "A localization theorem for the planar {Coulomb} gas in an external field", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--21", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP613", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-localization-theorem-for-the-planar-Coulomb-gas-in-an/10.1214/21-EJP613.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Coulomb gas; droplet; external potential; Localization", } @Article{Bovier:2021:MDC, author = "Anton Bovier and Saeda Marello and Elena Pulvirenti", title = "Metastability for the dilute {Curie--Weiss} model with {Glauber} dynamics", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--38", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP610", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37; 82B20; 82B44", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Metastability-for-the-dilute-CurieWeiss-model-with-Glauber-dynamics/10.1214/21-EJP610.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Erd{\H{o}}s--R{\'e}nyi random graph; Glauber dynamics; metastability; randomly dilute Curie--Weiss model", } @Article{Gotze:2021:CIP, author = "Friedrich G{\"o}tze and Holger Sambale and Arthur Sinulis", title = "Concentration inequalities for polynomials in $ \alpha $-sub-exponential random variables", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--22", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP606", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60E15; 46E30; 46N30", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Concentration-inequalities-for-polynomials-in-%ce%b1-sub-exponential-random-variables/10.1214/21-EJP606.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "concentration of measure phenomenon; Hanson-Wright inequality; Orlicz norms; Poisson chaos; sub-exponential random variables", } @Article{Collet:2021:CRM, author = "Francesca Collet and Fabrizio Leisen and Steen Thorbj{\o}rnsen", title = "Completely random measures and {L{\'e}vy} bases in free probability", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--41", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP620", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "46L54; 60E07; 60G57", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Completely-random-measures-and-L%c3%a9vy-bases-in-free-probability/10.1214/21-EJP620.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "free completely random measure; free infinite divisibility; free L{\'e}vy basis; L{\'e}vy-It{\^o} type decomposition", } @Article{Werner:2021:CPR, author = "Florian Werner", title = "Concatenation and pasting of right processes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--21", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP611", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J40; 60J45", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Concatenation-and-pasting-of-right-processes/10.1214/21-EJP611.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "concatenation; Markov processes; pasting; Right processes", } @Article{Hayashi:2021:SSL, author = "Kohei Hayashi", title = "Spatial-segregation limit for exclusion processes with two components under unbalanced reaction", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--36", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP621", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Spatial-segregation-limit-for-exclusion-processes-with-two-components-under/10.1214/21-EJP621.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "hydrodynamics limit; Interacting particle system", } @Article{Weber:2021:EII, author = "Frederic Weber", title = "Entropy-information inequalities under curvature-dimension conditions for continuous-time {Markov} chains", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--31", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP627", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J27; 47D07; 39A12", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Entropy-information-inequalities-under-curvature-dimension-conditions-for-continuous-time/10.1214/21-EJP627.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "curvature-dimension inequalities; diameter bounds; Entropy; exponential integrability of Lipschitz functions; Fisher information; Markov chain; modified Nash inequality; ultracontractive bounds", } @Article{deTiliere:2021:ZDM, author = "B{\'e}atrice de Tili{\`e}re", title = "The {$Z$}-Dirac and massive {Laplacian} operators in the {$Z$}-invariant {Ising} model", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--86", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP601", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B20; 82B23; 33E05; 05A19", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-Z-Dirac-and-massive-Laplacian-operators-in-the-Z/10.1214/21-EJP601.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Dimer model; discrete massive harmonic and holomorphic functions; Ising model; massive Laplacian and Dirac operators; spanning forests and spanning trees; Z-invariance", } @Article{Chelkak:2021:CML, author = "Dmitry Chelkak and Yijun Wan", title = "On the convergence of massive loop-erased random walks to massive {SLE(2)} curves", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--35", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP615", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B20", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-the-convergence-of-massive-loop-erased-random-walks-to/10.1214/21-EJP615.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60Dxx; loop-erased random walks; massive SLE curves", } @Article{Basse-OConnor:2021:PVF, author = "Andreas Basse-O'Connor and Vytaut{\.e} Pilipauskait{\.e} and Mark Podolskij", title = "Power variations for fractional type infinitely divisible random fields", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--35", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP617", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60G60; 60G22; 60G10; 60G57", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Power-variations-for-fractional-type-infinitely-divisible-random-fields/10.1214/21-EJP617.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "fractional fields; infill asymptotics; limit theorems; moving averages; power variation; stable convergence", } @Article{Grahovac:2021:IIV, author = "Danijel Grahovac and Nikolai N. Leonenko and Murad S. Taqqu", title = "Intermittency and infinite variance: the case of integrated {supOU} processes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--31", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP623", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60G52; 60G10", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Intermittency-and-infinite-variance--the-case-of-integrated-supOU/10.1214/21-EJP623.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "absolute moments; infinite variance; limit theorems; Ornstein--Uhlenbeck process; supOU processes", } @Article{Stivanello:2021:LTL, author = "Samuele Stivanello and Gianmarco Bet and Alessandra Bianchi and Marco Lenci and Elena Magnanini", title = "Limit theorems for {L{\'e}vy} flights on a {$1$D} {L{\'e}vy} random medium", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--25", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP626", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 60G55; 60F17; 82C41; 60G51", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Limit-theorems-for-L%c3%a9vy-flights-on-a-1D-L%c3%a9vy-random/10.1214/21-EJP626.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Anomalous diffusion; L{\'e}vy flights; L{\'e}vy random medium; random walk on point process; Stable distributions; Stable processes", } @Article{Profeta:2021:AUS, author = "Christophe Profeta", title = "The area under a spectrally positive stable excursion and other related processes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--21", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP618", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G52; 60G18; 60E10", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-area-under-a-spectrally-positive-stable-excursion-and-other/10.1214/21-EJP618.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Meander; normalized excursion; Stable processes", } @Article{Jalowy:2021:RCP, author = "Jonas Jalowy", title = "Rate of convergence for products of independent non-{Hermitian} random matrices", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--24", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP625", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 41A25", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Rate-of-convergence-for-products-of-independent-non-Hermitian-random/10.1214/21-EJP625.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "circular law; Ginibre matrices; Logarithmic potential; Meijer-G function; products of non-Hermitian random matrices; rate of convergence", } @Article{Behme:2021:LKE, author = "Anita Behme and Alexander Lindner and Jana Reker", title = "On the law of killed exponential functionals", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--35", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP616", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60E07; 60E10; 60J35; 46N30", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-the-law-of-killed-exponential-functionals/10.1214/21-EJP616.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Density; exponential functional; generalised Ornstein--Uhlenbeck process; infinitesimal generator; killing; L{\'e}vy processes", } @Article{Belloum:2021:ASR, author = "Mohamed Ali Belloum and Bastien Mallein", title = "Anomalous spreading in reducible multitype branching {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--39", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP629", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60G55; 60G70; 92D25", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Anomalous-spreading-in-reducible-multitype-branching-Brownian-motion/10.1214/21-EJP629.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "anomalous spreading; Branching Brownian motion; Brownian motion; Extremal process; multitype branching process", } @Article{Nica:2021:IDL, author = "Mihai Nica", title = "Intermediate disorder limits for multi-layer semi-discrete directed polymers", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--50", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP614", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82D60", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Intermediate-disorder-limits-for-multi-layer-semi-discrete-directed-polymers/10.1214/21-EJP614.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "KPZ; non-intersecting random walks; random polymers", } @Article{Collevecchio:2021:NRV, author = "Andrea Collevecchio and Xiaolin Zeng", title = "A note on recurrence of the Vertex reinforced jump process and fractional moments localization", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--16", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP609", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-note-on-recurrence-of-the-Vertex-reinforced-jump-process/10.1214/21-EJP609.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Localization; recurrence; Vertex-reinforced jump process", } @Article{Ahmadi:2021:BSD, author = "Mahdi Ahmadi and Alexandre Popier and Ali Devin Sezer", title = "Backward stochastic differential equations with non-{Markovian} singular terminal conditions for general driver and filtration", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--27", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP619", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G40; 60G99; 60H99; 65M80", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Backward-stochastic-differential-equations-with-non-Markovian-singular-terminal-conditions/10.1214/21-EJP619.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "backward stochastic differential equation; continuity problem; density of hitting time; Green's function; singularity", } @Article{deCatelan:2021:FGP, author = "Jacques de Catelan and Pierre-Lo{\"\i}c M{\'e}liot", title = "Fluctuations of the {Gromov--Prohorov} sample model", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--37", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP634", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B10; 60B05; 60F05", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Fluctuations-of-the-GromovProhorov-sample-model/10.1214/21-EJP634.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "combinatorics of the cumulants of random variables; discrete approximation of metric spaces; Gromov--Prohorov topology", } @Article{Dolgopyat:2021:EBD, author = "Dmitry Dolgopyat and Bassam Fayad and Maria Saprykina", title = "Erratic behavior for $1$-dimensional random walks in a {Liouville} quasi-periodic environment", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--36", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP622", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60F15; 37C05; 37A45", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Erratic-behavior-for-1-dimensional-random-walks-in-a-Liouville/10.1214/21-EJP622.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Liouville phenomena; Localization; random walks in random environment; random walks in random potential", } @Article{Assing:2021:ETF, author = "Sigurd Assing and John Herman", title = "Extension technique for functions of diffusion operators: a stochastic approach", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--32", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP624", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J45; 60J60; 60J55; 35J25; 35J70; 47G20", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Extension-technique-for-functions-of-diffusion-operators--a-stochastic/10.1214/21-EJP624.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Dirichlet-to-Neumann map; elliptic equation; Krein strings; trace process", } @Article{Ancona:2021:ZSS, author = "Michele Ancona and Thomas Letendre", title = "Zeros of smooth stationary {Gaussian} processes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--81", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP637", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60F15; 60F17; 60F25; 60G15; 60G55; 60G57", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Zeros-of-smooth-stationary-Gaussian-processes/10.1214/21-EJP637.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; central moments; clustering; Gaussian process; k-point function; Kac--Rice formula; Law of Large Numbers", } @Article{Deslandes:2021:LLL, author = "Cl{\'e}ment Deslandes and Christian Houdr{\'e}", title = "On the limiting law of the length of the longest common and increasing subsequences in random words with arbitrary distribution", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--27", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP612", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05A05; 60C05; 60F05", bibdate = "Fri May 21 05:21:04 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-the-limiting-law-of-the-length-of-the-longest/10.1214/21-EJP612.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Last passage percolation; longest common subsequences; longest increasing subsequences; optimal alignment; random matrices; random words; weak convergence", } @Article{Lember:2021:EFS, author = "J{\"u}ri Lember and Joonas Sova", title = "Exponential forgetting of smoothing distributions for pairwise {Markov} models", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--30", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP628", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J05; 60J55", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Exponential-forgetting-of-smoothing-distributions-for-pairwise-Markov-models/10.1214/21-EJP628.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Hidden Markov models; Markov models; smoothing probabilities", } @Article{Huang:2021:PDD, author = "Xing Huang", title = "Path-distribution dependent {SDEs} with singular coefficients", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--21", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP630", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G44", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Path-distribution-dependent-SDEs-with-singular-coefficients/10.1214/21-EJP630.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60H1075; Harnack inequality; Krylov's estimate; Path-distribution dependent SDEs; Zvonkin's transform", } @Article{Kozitsky:2021:MPI, author = "Yuri Kozitsky and Michael R{\"o}ckner", title = "A {Markov} process for an infinite interacting particle system in the continuum", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--53", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP631", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J25; 60J75; 60G55; 35Q84", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-Markov-process-for-an-infinite-interacting-particle-system-in/10.1214/21-EJP631.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Fokker--Planck equation; martingale solution; Measure-valued Markov process; point process; stochastic semigroup", } @Article{Allan:2021:RFP, author = "Andrew L. Allan", title = "Robust filtering and propagation of uncertainty in hidden {Markov} models", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--37", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP633", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G35; 60L50; 60L90", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Robust-filtering-and-propagation-of-uncertainty-in-hidden-Markov-models/10.1214/21-EJP633.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Filtering; Hidden Markov model; parameter uncertainty; pathwise optimal control; Rough paths", } @Article{Bates:2021:FPL, author = "Erik Bates", title = "Full-path localization of directed polymers", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--24", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP641", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60G15; 60G17; 82B44; 82D30; 82D60", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Full-path-localization-of-directed-polymers/10.1214/21-EJP641.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Directed polymers; Gaussian disorder; path localization; Replica overlap", } @Article{Nejjar:2021:DPT, author = "Peter Nejjar", title = "Dynamical phase transition of {ASEP} in the {KPZ} regime", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--20", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP642", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Dynamical-phase-transition-of-ASEP-in-the-KPZ-regime/10.1214/21-EJP642.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "ASEP; dynamical phase transition; KPZ universality", } @Article{Altman:2021:BSG, author = "Henri Elad Altman", title = "{Bessel} {SPDEs} with general {Dirichlet} boundary conditions", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--36", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP632", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60H17", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Bessel-SPDEs-with-general-Dirichlet-boundary-conditions/10.1214/21-EJP632.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bessel processes; Dirichlet forms; integration by parts formulae; Local times; renormalisation; Singular SPDEs", } @Article{Lochowski:2021:LTT, author = "Rafa{\l} M. {\L}ochowski and Jan Ob{\l}{\'o}j and David J. Pr{\"o}mel and Pietro Siorpaes", title = "Local times and {Tanaka--Meyer} formulae for c{\`a}dl{\`a}g paths", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--29", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP638", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "26A99; 60J60; 60H05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Local-times-and-TanakaMeyer-formulae-for-c%c3%a0dl%c3%a0g-paths/10.1214/21-EJP638.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "c{\`a}dl{\`a}g path; F{\"o}llmer--It{\^o} formula; Local time; pathwise stochastic integration; pathwise Tanaka formula; Semimartingale", } @Article{Andrieu:2021:SHP, author = "Christophe Andrieu and Paul Dobson and Andi Q. Wang", title = "Subgeometric hypocoercivity for piecewise-deterministic {Markov} process {Monte Carlo} methods", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--26", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP643", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J25; 65C05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Subgeometric-hypocoercivity-for-piecewise-deterministic-Markov-process-Monte-Carlo-methods/10.1214/21-EJP643.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "hypocoercivity; Markov chain Monte Carlo; piecewise-deterministic Markov process; subgeometric convergence", } @Article{Botero:2021:LDP, author = "Alonso Botero and Matthias Christandl and P{\'e}ter Vrana", title = "Large deviation principle for moment map estimation", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--23", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP636", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F10; 22E46; 53D20; 81P50", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Large-deviation-principle-for-moment-map-estimation/10.1214/21-EJP636.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "compact Lie group; large deviation principle; moment map; quantum measurement", } @Article{Senizergues:2021:GWR, author = "Delphin S{\'e}nizergues", title = "Geometry of weighted recursive and affine preferential attachment trees", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--56", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP640", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J05; 05C05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Geometry-of-weighted-recursive-and-affine-preferential-attachment-trees/10.1214/21-EJP640.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "limit theorems; preferential attachment; profile of random trees; weighted recursive trees", } @Article{Barashkov:2021:MGT, author = "Nikolay Barashkov and Massimiliano Gubinelli", title = "The {$ \Phi_3^4 $} measure via {Girsanov}'s theorem", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--29", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP635", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "81T08; 60H30; 60L40", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-%ce%a634-measure-via-Girsanovs-theorem/10.1214/21-EJP635.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bou {\'e}-Dupuis formula; Contructive Euclidean Quantum Field Theory; Paracontrolled calculus", } @Article{Kozma:2021:PLD, author = "Gady Kozma and Ron Peled", title = "Power-law decay of weights and recurrence of the two-dimensional {VRJP}", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--19", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP639", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60K35; 81T25; 81T60", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Power-law-decay-of-weights-and-recurrence-of-the-two/10.1214/21-EJP639.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "decay of correlations; Random walk in random environment; supersymmetry; Vertex-reinforced jump process", } @Article{Ocafrain:2021:CQS, author = "William O{\c{c}}afrain", title = "Convergence to quasi-stationarity through {Poincar{\'e}} inequalities and {Bakry--{\'E}mery} criteria", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--30", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP644", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B10; 60F99; 60J25; 60J50", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Convergence-to-quasi-stationarity-through-Poincar%c3%a9-inequalities-and-Bakry-%c3%89mery/10.1214/21-EJP644.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "1-Wasserstein distance; 39B62; 60J60.; Absorbed Markov processes; Bakry-{\'E}mery condition; multi-dimensional diffusion processes; Poincar{\'e} inequality; quasi-stationary distribution", } @Article{Bercu:2021:SAA, author = "Bernard Bercu and Manon Costa and S{\'e}bastien Gadat", title = "Stochastic approximation algorithms for superquantiles estimation", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--29", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP648", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "62L20; 60F05; 62P05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Stochastic-approximation-algorithms-for-superquantiles-estimation/10.1214/21-EJP648.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "conditional value-at-risk; limit theorems; quantile and superquantile; stochastic approximation", } @Article{Chen:2021:SBS, author = "Xin Chen and Wenjie Ye", title = "A study of backward stochastic differential equation on a {Riemannian} manifold", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--31", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP649", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H30; 58J65", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-study-of-backward-stochastic-differential-equation-on-a-Riemannian/10.1214/21-EJP649.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "backward stochastic differential equation; Riemannian manifold; second fundamental form", } @Article{Iyer:2021:PAC, author = "Srikanth K. Iyer and Sanjoy Kr Jhawar", title = "{Poisson} approximation and connectivity in a scale-free random connection model", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--23", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP651", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 60G70; 60G55; 05C80; 05C82", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Poisson-approximation-and-connectivity-in-a-scale-free-random-connection/10.1214/21-EJP651.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "connectivity; inhomogeneous random connection model; Poisson convergence; Poisson point process; scale-free networks; Stein's method", } @Article{Song:2021:HDC, author = "Jian Song and Jianfeng Yao and Wangjun Yuan", title = "High-dimensional central limit theorems for a class of particle systems", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--33", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP646", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60F05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/High-dimensional-central-limit-theorems-for-a-class-of-particle/10.1214/21-EJP646.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; Dyson's Brownian motion; matrix-valued Ornstein--Uhlenbeck process; Particle system; squared Bessel particle system; Wishart process", } @Article{Broutin:2021:SSR, author = "Nicolas Broutin and Henning Sulzbach", title = "Self-similar real trees defined as fixed points and their geometric properties", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--50", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP647", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05; 60F17; 05C05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Self-similar-real-trees-defined-as-fixed-points-and-their/10.1214/21-EJP647.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "continuum real tree; fractal dimension; self-similarity; Stochastic fixed point equation", } @Article{Hernandez:2021:UAW, author = "Camilo Hern{\'a}ndez and Dylan Possama{\"\i}", title = "A unified approach to well-posedness of type-{I} backward stochastic {Volterra} integral equations", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--35", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP653", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "93E20; 35F21; 35Q93", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-unified-approach-to-well-posedness-of-type-I-backward/10.1214/21-EJP653.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Backward stochastic Volterra integral equations; consistent planning; equilibrium Hamilton--Jacobi--Bellman equation; representation of partial differential equations; Time inconsistency", } @Article{Kim:2021:AON, author = "Edward Kim and Tianyang Nie and Marek Rutkowski", title = "{American} options in nonlinear markets", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--41", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP658", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "91G40; 60J28; 91G30; 60H30; 60H10", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/American-options-in-nonlinear-markets/10.1214/21-EJP658.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "American option; nonlinear evaluation; nonlinear market; Reflected BSDE", } @Article{Klimsiak:2021:RBT, author = "Tomasz Klimsiak and Maurycy Rzymowski", title = "Reflected {BSDEs} with two optional barriers and monotone coefficient on general filtered space", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--24", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP655", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10; 60G40", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Reflected-BSDEs-with-two-optional-barriers-and-monotone-coefficient-on/10.1214/21-EJP655.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Dynkin games; nonlinear expectation; optional barriers; processes with regulated trajectories; reflected backward stochastic differential equation", } @Article{FitzGerald:2021:IMP, author = "Will FitzGerald", title = "The invariant measure of {PushASEP} with a wall and point-to-line last passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--26", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP661", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60C05; 60J45", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-invariant-measure-of-PushASEP-with-a-wall-and-point/10.1214/21-EJP661.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "interacting particle systems; non-colliding random walks; point-to-line last passage percolation; symplectic Schur functions", } @Article{Steiner:2021:FKA, author = "Cl{\'e}ment Steiner", title = "A {Feynman--Kac} approach for logarithmic {Sobolev} inequalities", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--19", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP656", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "47D08; 60J60", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-Feynman--Kac-approach-for-logarithmic-Sobolev-inequalities/10.1214/21-EJP656.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "39B62; Diffusion processes; Feynman--Kac semigroups; logarithmic Sobolev inequalities; perturbed functional inequalities", } @Article{Gwynne:2021:JSL, author = "Ewain Gwynne and Nina Holden and Xin Sun", title = "Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--58", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP659", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60F17; 60J67; 60G57", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Joint-scaling-limit-of-site-percolation-on-random-triangulations-in/10.1214/21-EJP659.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian map; Cardy embedding; Conformal Loop Ensemble; Liouville quantum gravity; mating of trees; Peanosphere; percolation; Schramm-Loewner evolution; uniform triangulations", } @Article{Marguet:2021:LTB, author = "Aline Marguet and Charline Smadi", title = "Long time behaviour of continuous-state nonlinear branching processes with catastrophes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--32", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP664", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60J85; 60H10", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Long-time-behaviour-of-continuous-state-nonlinear-branching-processes-with/10.1214/21-EJP664.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "absorption; continuous-time and space branching Markov processes; explosion; jumps processes; Long-time behaviour", } @Article{Lupu:2021:IRK, author = "Titus Lupu and Christophe Sabot and Pierre Tarr{\`e}s", title = "Inverting the {Ray--Knight} identity on the line", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--25", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP657", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G15; 60J60; 60K35; 60K37; 60J55; 81T25; 81T60", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Inverting-the-Ray-Knight-identity-on-the-line/10.1214/21-EJP657.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gaussian free field; isomorphism theorems; Local time; self-interacting diffusion", } @Article{Morrison:2021:STB, author = "Natasha Morrison and Jonathan A. Noel", title = "A sharp threshold for bootstrap percolation in a random hypergraph", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--85", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP650", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60G42; 05C65", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-sharp-threshold-for-bootstrap-percolation-in-a-random-hypergraph/10.1214/21-EJP650.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bootstrap percolation; differential equations method; hypergraphs; Martingales; sharp threshold", } @Article{Glatzel:2021:SRW, author = "Tabea Glatzel and Jan Nagel", title = "The speed of random walk on {Galton--Watson} trees with vanishing conductances", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--19", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP645", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60F15; 60J80; 60K40", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-speed-of-random-walk-on-Galton--Watson-trees-with/10.1214/21-EJP645.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Effective velocity; Galton--Watson trees; Random walk in random environment", } @Article{Benjamini:2021:IEU, author = "Itai Benjamini and {\'A}d{\'a}m Tim{\'a}r", title = "Invariant embeddings of unimodular random planar graphs", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--18", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP665", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 60K99", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Invariant-embeddings-of-unimodular-random-planar-graphs/10.1214/21-EJP665.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "invariant embedding; random planar graphs; unimodular embedding", } @Article{Belinschi:2021:OEN, author = "Serban Belinschi and Charles Bordenave and Mireille Capitaine and Guillaume C{\'e}bron", title = "Outlier eigenvalues for non-{Hermitian} polynomials in independent i.i.d. matrices and deterministic matrices", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--37", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP666", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "15B52; 60B20; 46L54; 60F05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Outlier-eigenvalues-for-non-Hermitian-polynomials-in-independent-iid-matrices/10.1214/21-EJP666.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "15A18; Free probability; random matrices", } @Article{Kai:2021:GFJ, author = "Hirotaka Kai and Atsushi Takeuchi", title = "Gradient formulas for jump processes on manifolds", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--15", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP660", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J76; 58J65; 60H07; 60H10", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Gradient-formulas-for-jump-processes-on-manifolds/10.1214/21-EJP660.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Integration by parts formulas; jump processes on manifolds; Stochastic differential equations with jumps", } @Article{Guerrero:2021:ASW, author = "Raul Bola{\~n}os Guerrero and David Nualart and Guangqu Zheng", title = "Averaging 2d stochastic wave equation", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--32", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP672", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60H07; 60G15; 60F05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Averaging-2d-stochastic-wave-equation/10.1214/21-EJP672.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; Malliavin-Stein method; Riesz kernel; Stochastic wave equation", } @Article{Roberts:2021:GPD, author = "Matthew I. Roberts and Jason Schweinsberg", title = "A {Gaussian} particle distribution for branching {Brownian} motion with an inhomogeneous branching rate", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--76", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP673", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 92D15; 92D25", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-Gaussian-particle-distribution-for-branching-Brownian-motion-with-an/10.1214/21-EJP673.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Branching Brownian motion; Evolution; fitness; Gaussian traveling wave", } @Article{Takei:2021:ASB, author = "Masato Takei", title = "Almost sure behavior of linearly edge-reinforced random walks on the half-line", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--18", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP674", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Almost-sure-behavior-of-linearly-edge-reinforced-random-walks-on/10.1214/21-EJP674.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "random walks in random environment; reinforced random walks", } @Article{Cichomski:2021:MDA, author = "Stanis{\l}aw Cichomski and Adam Os{\k{e}}kowski", title = "The maximal difference among expert's opinions", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--17", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP675", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60E15", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-maximal-difference-among-experts-opinions/10.1214/21-EJP675.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Coherent; joint distribution of conditional expectations; opinion; sharp inequality", } @Article{Bechtold:2021:LLN, author = "Florian Bechtold and Fabio Coppini", title = "A law of large numbers for interacting diffusions via a mild formulation", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--27", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP671", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60F05; 60H20; 60H15; 60L90", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-law-of-large-numbers-for-interacting-diffusions-via-a/10.1214/21-EJP671.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Interacting particle system; McKean--Vlasov; Rough paths; self-normalized processes; semigroup approach; Stochastic differential equations", } @Article{Lamarre:2021:SOD, author = "Pierre Yves Gaudreau Lamarre", title = "Semigroups for one-dimensional {Schr{\"o}dinger} operators with multiplicative {Gaussian} noise", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--47", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP654", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "47H40; 47D08; 60J55", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Semigroups-for-one-dimensional-Schr%c3%b6dinger-operators-with-multiplicative-Gaussian-noise/10.1214/21-EJP654.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "random Schr{\"o}dinger operators; Gaussian noise; Schr{\"o}dinger semigroups; Feynman--Kac formula", } @Article{Brandenberger:2021:HSN, author = "Anna Brandenberger and Luc Devroye and Tommy Reddad", title = "The {Horton}--Strahler number of conditioned {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--29", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP678", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05; 60J80; 05C05; 60F05", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-HortonStrahler-number-of-conditioned-GaltonWatson-trees/10.1214/21-EJP678.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "branching processes; Galton--Watson trees; Horton--Strahler number; probabilistic analysis; Register function", } @Article{Deligiannidis:2021:BRR, author = "George Deligiannidis and S{\'e}bastien Gou{\"e}zel and Zemer Kosloff", title = "The boundary of the range of a random walk and the {F{\o}lner} property", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--39", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP667", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60G50; 20F65", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-boundary-of-the-range-of-a-random-walk-and/10.1214/21-EJP667.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "F{\o}lner property; Random walk; range", } @Article{Kumar:2021:EMT, author = "Chaman Kumar and Neelima", title = "On explicit {Milstein}-type scheme for {McKean--Vlasov} stochastic differential equations with super-linear drift coefficient", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--32", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP676", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "65C30; 65C35; 65C05; 60H35", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-explicit-Milstein-type-scheme-for-McKeanVlasov-stochastic-differential-equations/10.1214/21-EJP676.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "explicit Milstein scheme; McKean--Vlasov SDE; propagation of chaos; rate of strong convergence; super-linear coefficient", } @Article{Lashari:2021:DS, author = "Abid Ali Lashari and Ana Serafimovi{\'c} and Pieter Trapman", title = "The duration of a supercritical", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--49", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP679", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 92D30; 05C80; 60J80", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-duration-of-a-supercritical-SIR-epidemic-on-a-configuration/10.1214/21-EJP679.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "branching process approximation; first passage percolation; SIR epidemics; time to extinction; vaccination", } @Article{Andjel:2021:ZRP, author = "Enrique Andjel and In{\'e}s Armend{\'a}riz and Milton Jara", title = "Zero-range processes with rapidly growing rates", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--29", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP670", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82C22", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Zero-range-processes-with-rapidly-growing-rates/10.1214/21-EJP670.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "construction of dynamics; Invariant measures; Martingales; superlinear rates; Zero-range process", } @Article{Benth:2021:IDP, author = "Fred Espen Benth and Fabian A. Harang", title = "Infinite dimensional pathwise {Volterra} processes driven by {Gaussian} noise --- Probabilistic properties and applications", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--42", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP683", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H05; 60H20; 45D05; 34A12", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Infinite-dimensional-pathwise-Volterra-processes-driven-by-Gaussian-noise-/10.1214/21-EJP683.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Covariance operator; Fractional differential equations; Gaussian processes; Hilbert space; infinite dimensional stochastic analysis; rough path integration; rough volatility models; Volterra integral equations", } @Article{Andriopoulos:2021:IPR, author = "George Andriopoulos", title = "Invariance principles for random walks in random environment on trees", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--38", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP687", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60F17; 82D30; 60K35", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Invariance-principles-for-random-walks-in-random-environment-on-trees/10.1214/21-EJP687.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "biased random walk; Branching random walk; diffusion in random potential; Galton--Watson tree; Random walk in random environment; self-reinforcement; Sinai's regime", } @Article{Pakkanen:2021:LTT, author = "Mikko S. Pakkanen and Riccardo Passeggeri and Orimar Sauri and Almut E. D. Veraart", title = "Limit theorems for trawl processes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--36", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP652", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17; 60G10; 60G57", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Limit-theorems-for-trawl-processes/10.1214/21-EJP652.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Functional limit theorem; moving average; partial sum; stable convergence; trawl process", } @Article{Shen:2021:DTS, author = "Yi Shen and Zhenyuan Zhang", title = "On discrete-time self-similar processes with stationary increments", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--24", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP689", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G18; 60G10", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-discrete-time-self-similar-processes-with-stationary-increments/10.1214/21-EJP689.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "discrete-time; Self-similar; Stationary increments", } @Article{Agarwal:2021:VMT, author = "Pooja Agarwal and Mackenzie Simper and Rick Durrett", title = "The $q$-voter model on the torus", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--33", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP682", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-q-voter-model-on-the-torus/10.1214/21-EJP682.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "ODE limit; renormalization; voter model perturbation", } @Article{Barrera:2021:CPT, author = "Gerardo Barrera and Michael A. H{\"o}gele and Juan Carlos Pardo", title = "The cutoff phenomenon in total variation for nonlinear {Langevin} systems with small layered stable noise", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--76", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP685", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "37A25; 37A30; 60F05; 60G51; 60G52; 65C30", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-cutoff-phenomenon-in-total-variation-for-nonlinear-Langevin-systems/10.1214/21-EJP685.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Cutoff phenomenon; abrupt thermalization; exponential ergodicity; Stable L{\'e}vy processes; local limit theorem; nonlinear coupling; short coupling; total variation distance; counterexample to Slutsky's lemma in total variation; H{\"o}lder continuity of the characteristic exponent", } @Article{Cormier:2021:HBM, author = "Quentin Cormier and Etienne Tanr{\'e} and Romain Veltz", title = "{Hopf} bifurcation in a mean-field model of spiking neurons", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--40", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP688", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 35B10; 35B32; 60H10", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Hopf-bifurcation-in-a-Mean-Field-model-of-spiking-neurons/10.1214/21-EJP688.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Hopf bifurcation; long time behavior; McKean--Vlasov SDE; Mean-field interaction; Piecewise deterministic Markov process; Volterra integral equation", } @Article{Rackauskas:2021:AMW, author = "Alfredas Ra{\v{c}}kauskas and Charles Suquet", title = "On the asymptotic of the maximal weighted increment of a random walk with regularly varying jumps: the boundary case", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--31", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP691", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 60G70", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-the-asymptotic-of-the-maximal-weighted-increment-of-a/10.1214/21-EJP691.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "maximal increment; Random walk; regularly varying random variables", } @Article{Coquille:2021:SIB, author = "Loren Coquille and Anna Kraut and Charline Smadi", title = "Stochastic individual-based models with power law mutation rate on a general finite trait space", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--37", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP693", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "92D25; 60J80; 92D15; 37N25", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Stochastic-individual-based-models-with-power-law-mutation-rate-on/10.1214/21-EJP693.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "adaptive dynamics; birth and death processes; competitive Lotka--Volterra systems; coupling; Eco-evolution; finite graph; selective sweep", } @Article{Dubach:2021:ESS, author = "Guillaume Dubach", title = "On eigenvector statistics in the spherical and truncated unitary ensembles", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--29", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP686", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 15B52", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-eigenvector-statistics-in-the-spherical-and-truncated-unitary-ensembles/10.1214/21-EJP686.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "eigenvectors overlaps; Non-Hermitian random matrices; spherical ensemble; truncated unitary matrices", } @Article{Carinci:2021:CPS, author = "Gioia Carinci and Cristian Giardin{\`a} and Frank Redig", title = "Consistent particle systems and duality", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--31", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP684", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60J25", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Consistent-particle-systems-and-duality/10.1214/21-EJP684.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "boundary driven systems; Duality; interacting particle systems; non-equilibrium stationary measure; Symmetric exclusion process; symmetric inclusion process", } @Article{Lupu:2021:ITD, author = "Titus Lupu", title = "Isomorphisms of $ \beta $-{Dyson}'s {Brownian} motion with {Brownian} local time", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--31", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP697", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "15B52; 60B20; 60J55; 60G15; 81T18", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Isomorphisms-of-%ce%b2-Dysons-Brownian-motion-with-Brownian-local-time/10.1214/21-EJP697.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Dyson's Brownian motion; Gaussian beta ensembles; Gaussian free field; isomorphism theorems; Local time; Permanental fields; topological expansion", } @Article{Seppalainen:2021:ECE, author = "Timo Sepp{\"a}l{\"a}inen and Xiao Shen", title = "Erratum to: {Coalescence estimates for the corner growth model with exponential weights}", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--4", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP714", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Seppalainen:2020:CEC}.", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Erratum-to--Coalescence-estimates-for-the-corner-growth-model/10.1214/21-EJP714.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "coalescence exit time; fluctuation exponent; Geodesic; Kardar-Parisi-Zhang; Last-passage percolation; random growth model", } @Article{Pene:2021:LTA, author = "Fran{\c{c}}oise P{\`e}ne", title = "Limit theorems for additive functionals of random walks in random scenery", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--46", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP696", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60F17; 60G15; 60G18; 60K37", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Limit-theorems-for-additive-functionals-of-random-walks-in-random/10.1214/21-EJP696.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian motion; central limit theorem; dynamical system; ergodicity; Infinite measure; local limit theorem; Local time; Random walk in random scenery", } @Article{Braun:2021:HFR, author = "Mathias Braun and Batu G{\"u}neysu", title = "Heat flow regularity, {Bismut--Elworthy--Li}'s derivative formula, and pathwise couplings on {Riemannian} manifolds with {Kato} bounded {Ricci} curvature", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--25", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP703", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "47D08; 53C21; 58J35; 58J65", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Heat-flow-regularity-BismutElworthyLis-derivative-formula-and-pathwise-couplings-on/10.1214/21-EJP703.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bismut--Elworthy--Li formula; coupling; Kato class; Ricci curvature", } @Article{Lopatto:2021:TBG, author = "Patrick Lopatto and Kyle Luh", title = "Tail bounds for gaps between eigenvalues of sparse random matrices", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--26", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP669", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Tail-bounds-for-gaps-between-eigenvalues-of-sparse-random-matrices/10.1214/21-EJP669.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "eigenvalue gap; Random matrix theory; sparse", } @Article{Iksanov:2021:LTD, author = "Alexander Iksanov and Anatolii Nikitin and Igor Samoilenko", title = "Limit theorems for discounted convergent perpetuities", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--25", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP705", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F15; 60F17; 60G50", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Limit-theorems-for-discounted-convergent-perpetuities/10.1214/21-EJP705.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "cluster set; functional central limit theorem; Law of the iterated logarithm; perpetuity; Strong law of large numbers", } @Article{Mijatovic:2021:LPS, author = "Aleksandar Mijatovi{\'c} and Veno Mramor", title = "{L{\'e}vy} processes on smooth manifolds with a connection", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--39", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP702", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51; 58J65; 60J25", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/L%c3%a9vy-processes-on-smooth-manifolds-with-a-connection/10.1214/21-EJP702.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "holonomy bundle; horizontal L{\'e}vy process; Linear connection; L{\'e}vy process on a smooth manifold; Marcus stochastic differential equation; stochastic anti-development; stochastic horizontal lift", } @Article{Betz:2021:SPT, author = "Volker Betz and Johannes Ehlert and Benjamin Lees and Lukas Roth", title = "Sharp phase transition for random loop models on trees", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--26", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP677", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Sharp-phase-transition-for-random-loop-models-on-trees/10.1214/21-EJP677.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60; phase transition; random interchange; Random loop model; Random Stirring", } @Article{Corso:2021:LDR, author = "Emilio Corso", title = "Large deviations for random walks on free products of finitely generated groups", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--22", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP695", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B15; 60F10; 60G50; 05C81", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Large-deviations-for-random-walks-on-free-products-of-finitely/10.1214/21-EJP695.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "cone types; free groups; Free Products; Gromov-hyperbolic groups; large deviations; Random walks; regular trees", } @Article{Dimitrov:2021:TBG, author = "Evgeni Dimitrov and Xiang Fang and Lukas Fesser and Christian Serio and Carson Teitler and Angela Wang and Weitao Zhu", title = "Tightness of {Bernoulli} {Gibbsian} line ensembles", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--93", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP698", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B41; 60J65", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Tightness-of-Bernoulli-Gibbsian-line-ensembles/10.1214/21-EJP698.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "avoiding random walks; Brownian motion; Gibbsian line ensembles", } @Article{Gapeev:2021:PME, author = "Pavel V. Gapeev and Monique Jeanblanc and Dongli Wu", title = "Projections of martingales in enlargements of {Brownian} filtrations under {Jacod}'s equivalence hypothesis", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--24", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP694", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G44; 60J65; 60G40; 60G35; 60H10; 91G40", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Projections-of-martingales-in-enlargements-of-Brownian-filtrations-under-Jacods/10.1214/21-EJP694.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian motion; changes of probability measures; conditional probability density; initial and progressive enlargements of filtrations; Jacod's equivalence hypothesis; predictable (martingale) representation property", } @Article{Baldassarri:2021:MLG, author = "Simone Baldassarri and Francesca Romana Nardi", title = "Metastability in a lattice gas with strong anisotropic interactions under {Kawasaki} dynamics", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--66", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP701", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10; 60K35; 82C20; 82C22; 82C26", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Metastability-in-a-lattice-gas-with-strong-anisotropic-interactions-under/10.1214/21-EJP701.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "critical droplet; Kawasaki dynamics; large deviations; lattice gas; metastability", } @Article{Freidlin:2021:ACM, author = "M. Freidlin and L. Koralov", title = "Averaging in the case of multiple invariant measures for the fast system", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--17", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP681", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "70K70; 70K65; 35B40; 34C29", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Averaging-in-the-case-of-multiple-invariant-measures-for-the/10.1214/21-EJP681.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "averaging; fast-slow system; gluing conditions; processes on graphs; simplex of invariant measures", } @Article{Kaur:2021:HOF, author = "Gursharn Kaur and Adrian R{\"o}llin", title = "Higher-order fluctuations in dense random graph models", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--36", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP708", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 05C80", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Higher-order-fluctuations-in-dense-random-graph-models/10.1214/21-EJP708.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "centered subgraph counts; central limit theorem; Gaussian Hilbert spaces; graphon", } @Article{Chen:2021:SES, author = "Le Chen and Davar Khoshnevisan and David Nualart and Fei Pu", title = "Spatial ergodicity for {SPDEs} via {Poincar{\'e}}-type inequalities", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--37", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP690", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 37A25; 60H07; 60G10", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Spatial-ergodicity-for-SPDEs-via-Poincar%c3%a9-type-inequalities/10.1214/21-EJP690.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "ergodicity; Malliavin calculus; Poincar{\'e}-type inequality; SPDEs", } @Article{Tang:2021:WUS, author = "Pengfei Tang", title = "Weights of uniform spanning forests on nonunimodular transitive graphs", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--62", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP709", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Weights-of-uniform-spanning-forests-on-nonunimodular-transitive-graphs/10.1214/21-EJP709.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Mass-transport principle; nonunimodular transitive graphs; uniform spanning forests", } @Article{Klaassen:2021:HID, author = "Chris A. J. Klaassen and Jon A. Wellner", title = "{Hardy}'s inequality and its descendants: a probability approach", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--34", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP711", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "26D15; 60E15", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Hardys-inequality-and-its-descendants-a-probability-approach/10.1214/21-EJP711.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Carleman's inequality; Copson's inequality; Hardy--Littlewood-Bliss inequality; Martingales; Muckenhoupt's inequality; P{\'o}lya-Knopp inequality; reverse Hardy inequality; Survival analysis", } @Article{Ahlberg:2021:RCQ, author = "Daniel Ahlberg and Daniel de la Riva and Simon Griffiths", title = "On the rate of convergence in quenched {Voronoi} percolation", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--26", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP712", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-the-rate-of-convergence-in-quenched-Voronoi-percolation/10.1214/21-EJP712.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Concentration; Noise sensitivity; Voronoi percolation", } @Article{Do:2021:RRR, author = "Yen Q. Do", title = "Real roots of random polynomials with coefficients of polynomial growth: a comparison principle and applications", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--45", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP719", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "30B20", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Real-roots-of-random-polynomials-with-coefficients-of-polynomial-growth/10.1214/21-EJP719.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "non-centered; non-zero mean; random polynomial; real root", } @Article{Berman:2021:PLW, author = "Robert J. Berman", title = "Priors leading to well-behaved {Coulomb} and {Riesz} gases versus zeroth-order phase transitions --- a potential-theoretic characterization", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--49", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP700", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60F10; 82B26; 31C40", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Priors-leading-to-well-behaved-Coulomb-and-Riesz-gases-versus/10.1214/21-EJP700.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "fine potential theory; large deviations; Phase transitions; statistical mechanics type models", } @Article{Collins-Woodfin:2021:OSS, author = "Elizabeth Collins-Woodfin", title = "Overlaps of a spherical spin glass model with microscopic external field", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--22", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP722", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Overlaps-of-a-spherical-spin-glass-model-with-microscopic-external/10.1214/21-EJP722.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "15; 60; 82; Sherrington--Kirkpatrick; Spin glass", } @Article{Fonseca-Mora:2021:SIR, author = "Christian A. Fonseca-Mora", title = "Stochastic integration with respect to cylindrical semimartingales", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--48", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP718", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H05; 60B11; 60G20; 60G48", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Stochastic-integration-with-respect-to-cylindrical-semimartingales/10.1214/21-EJP718.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "cylindrical semimartingales; locally convex spaces; Nuclear spaces; stochastic integrals; Tensor products", } @Article{Li:2021:ECC, author = "Bo Li and Xiaowen Zhou", title = "On the explosion of a class of continuous-state nonlinear branching processes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--25", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP715", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60J50", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/On-the-explosion-of-a-class-of-continuous-state-nonlinear/10.1214/21-EJP715.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Continuous-state branching process; explosion; Lamperti transform; spectrally positive L{\'e}vy process", } @Article{Pianoforte:2021:PAA, author = "Federico Pianoforte and Matthias Schulte", title = "{Poisson} approximation with applications to stochastic geometry", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--36", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP723", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60D05; 60G70; 60G55", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Poisson-approximation-with-applications-to-stochastic-geometry/10.1214/21-EJP723.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Chen-Stein method; exponential approximation; Extremes; Poisson approximation; Poisson-Voronoi tessellations; Runs; size-bias coupling; Stochastic geometry; U-statistics", } @Article{Benigni:2021:EDS, author = "Lucas Benigni and Sandrine P{\'e}ch{\'e}", title = "Eigenvalue distribution of some nonlinear models of random matrices", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--37", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP699", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "15B52; 62M45", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Eigenvalue-distribution-of-some-nonlinear-models-of-random-matrices/10.1214/21-EJP699.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "machine learning; neural networks; random matrices", } @Article{Dalmau:2021:WFM, author = "Joseba Dalmau", title = "The {Wright--Fisher} model for class--dependent fitness landscapes", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--44", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP704", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-WrightFisher-model-for-classdependent-fitness-landscapes/10.1214/21-EJP704.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "error threshold; invariant measure; large deviations; Quasispecies; Wright--Fisher model", } @Article{Berzin:2021:ELA, author = "Corinne Berzin", title = "Estimation of local anisotropy based on level sets", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--72", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP721", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "62G10; 53C65; 62F12; 60G60; 60G10; 60G15", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Estimation-of-local-anisotropy-based-on-level-sets/10.1214/21-EJP721.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Affine processes; Gaussian fields; isotropic processes; Level sets; Rice formulas for random fields; test of isotropy", } @Article{Berzunza:2021:TDB, author = "Gabriel Berzunza and Anja Sturm and Anita Winter", title = "Trait-dependent branching particle systems with competition and multiple offspring", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--41", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP707", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60J68; 60K35", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Trait-dependent-branching-particle-systems-with-competition-and-multiple-offspring/10.1214/21-EJP707.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "adaptive dynamics; branching process; competition-mutation dynamics; Darwinian evolution; Interacting particle system; limit theorem; nonlinear superprocesses", } @Article{Jourdain:2021:CLT, author = "Benjamin Jourdain and Alvin Tse", title = "Central limit theorem over non-linear functionals of empirical measures with applications to the mean-field fluctuation of interacting diffusions", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--34", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP720", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H30; 60H35; 65C30; 65C35; 35R06", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Central-limit-theorem-over-non-linear-functionals-of-empirical-measures/10.1214/21-EJP720.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; linear functional derivatives; mean-field diffusions; propagation of chaos", } @Article{Baccelli:2021:UHM, author = "Fran{\c{c}}ois Baccelli and Mir-Omid Haji-Mirsadeghi and Ali Khezeli", title = "Unimodular {Hausdorff} and {Minkowski} dimensions", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--64", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP692", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 05C63; 28A78", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Unimodular-Hausdorff-and-Minkowski-dimensions/10.1214/21-EJP692.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "infinite random graph; Mass transport principle; Palm calculus; point stationary point process; random discrete metric space; Random walks; self-similar sets", } @Article{Angst:2021:VSZ, author = "J{\"u}rgen Angst and Guillaume Poly", title = "Variations on {Salem--Zygmund} results for random trigonometric polynomials: application to almost sure nodal asymptotics", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--36", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP716", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "26C10; 30C15; 42A05; 60F17; 60G55", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Variations-on-SalemZygmund-results-for-random-trigonometric-polynomials--application/10.1214/21-EJP716.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "almost sure CLT; nodal asymptotics; random trigonometric polynomials; Universality", } @Article{Dumitrescu:2021:COS, author = "Roxana Dumitrescu and Marcos Leutscher and Peter Tankov", title = "Control and optimal stopping Mean Field Games: a linear programming approach", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--49", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP713", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "91A55; 91A13; 60G40", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Control-and-optimal-stopping-Mean-Field-Games--a-linear/10.1214/21-EJP713.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "continuous control; controlled/stopped martingale problem; infinite-dimensional linear programming; mean-field games; Optimal stopping; relaxed solutions", } @Article{Groisman:2021:RDB, author = "Pablo Groisman and Nahuel Soprano-Loto", title = "Rank dependent branching-selection particle systems", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--27", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP724", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J68; 60J80; 60G51", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Rank-dependent-branching-selection-particle-systems/10.1214/21-EJP724.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "branching-selection; Particle systems; propagation of chaos; Scaling limit; velocity", } @Article{Gantert:2021:TGW, author = "Nina Gantert and Nicos Georgiou and Dominik Schmid", title = "The {TASEP} on {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--38", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP725", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37; 60J75; 82C20", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/The-TASEP-on-GaltonWatson-trees/10.1214/21-EJP725.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "current; disentanglement; Exclusion process; invariant measure; Totally asymmetric simple exclusion process; trees", } @Article{Iksanov:2021:GFL, author = "Alexander Iksanov and Konrad Kolesko and Matthias Meiners", title = "{Gaussian} fluctuations and a law of the iterated logarithm for {Nerman}'s martingale in the supercritical general branching process", journal = j-ELECTRON-J-PROBAB, volume = "26", number = "18", pages = "1--22", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP727", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60F05; 60F17", bibdate = "Thu Mar 23 15:19:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Gaussian-fluctuations-and-a-law-of-the-iterated-logarithm-for/10.1214/21-EJP727.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "asymptotic fluctuations; functional central limit theorem; Law of the iterated logarithm; Nerman's martingale; supercritical general branching process", } @Article{Bates:2022:HDS, author = "Erik Bates and Shirshendu Ganguly and Alan Hammond", title = "{Hausdorff} dimensions for shared endpoints of disjoint geodesics in the directed landscape", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--44", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP706", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 28A80; 60G15; 60G57; 60K37; 82B44", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Hausdorff-dimensions-for-shared-endpoints-of-disjoint-geodesics-in-the/10.1214/21-EJP706.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Airy sheet; Brownian last passage percolation; directed landscape; geodesics; Polymers", } @Article{Heiny:2022:TST, author = "Johannes Heiny and Samuel Johnston and Joscha Prochno", title = "Thin-shell theory for rotationally invariant random simplices", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--41", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP734", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 52A23; 60D05; 60B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Thin-shell-theory-for-rotationally-invariant-random-simplices/10.1214/21-EJP734.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; high dimension; logarithmic volume; Random matrix; random simplex; Stochastic geometry", } @Article{Cerny:2022:SSC, author = "Ale{\v{s}} {\v{C}}ern{\'y} and Johannes Ruf", title = "Simplified stochastic calculus via semimartingale representations", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP729", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G07; 60G44; 60G48; 60H05; 60H05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Simplified-stochastic-calculus-via-semimartingale-representations/10.1214/21-EJP729.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "complex-valued process; generalized Yor formula; It{\^o} formula; semimartingale representation; {\'E}mery formula", } @Article{Jelito:2022:RSO, author = "Damian Jelito and {\L}ukasz Stettner", title = "Risk-sensitive optimal stopping with unbounded terminal cost function", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--30", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP736", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "93E20; 60G40; 49J21", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Risk-sensitive-optimal-stopping-with-unbounded-terminal-cost-function/10.1214/21-EJP736.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bellman equation; dynamic programming principle; Feller-Markov process; Optimal stopping; unbounded cost function", } @Article{Little:2022:NRE, author = "Alex Little and Francesco Mezzadri and Nick Simm", title = "On the number of real eigenvalues of a product of truncated orthogonal random matrices", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP732", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "15B52; 60B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-the-number-of-real-eigenvalues-of-a-product-of/10.1214/21-EJP732.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Products of random matrices; real eigenvalues; truncated orthogonal matrices", } @Article{Menezes:2022:VSS, author = "Ot{\'a}vio Menezes and Jonathon Peterson and Yongjia Xie", title = "Variable speed symmetric random walk driven by the simple symmetric exclusion process", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--14", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP735", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17; 60K35; 60K37", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Variable-speed-symmetric-random-walk-driven-by-the-simple-symmetric/10.1214/21-EJP735.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Exclusion process; Poisson equation; quenched functional central limit theorem; Random walk in random environment", } @Article{Lejay:2022:CGR, author = "Antoine Lejay", title = "Constructing general rough differential equations through flow approximations", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--24", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP717", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60L20; 34A06", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Constructing-general-rough-differential-equations-through-flow-approximations/10.1214/21-EJP717.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "aromatic Butcher series; Branched rough paths; rough differential equations", } @Article{Halberstam:2022:CRW, author = "Noah Halberstam and Tom Hutchcroft", title = "Collisions of random walks in dynamic random environments", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--18", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP738", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10; 05C81; 82C41; 60K37", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Collisions-of-random-walks-in-dynamic-random-environments/10.1214/21-EJP738.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Collisions; dynamic random environments; Dynamical percolation; Random walks", } @Article{Cordero:2022:TCA, author = "Fernando Cordero and Adri{\'a}n Gonz{\'a}lez Casanova and Jason Schweinsberg and Maite Wilke-Berenguer", title = "{$ \Lambda $}-coalescents arising in a population with dormancy", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--34", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP739", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J90; 60J80; 92D15; 92D25", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/%ce%9b-coalescents-arising-in-a-population-with-dormancy/10.1214/22-EJP739.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "dormancy; seed bank; {\textLambda}-coalescent", } @Article{Angelis:2022:SSC, author = "Tiziano De Angelis", title = "Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--41", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP733", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G40; 35R35; 60J60", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Stopping-spikes-continuation-bays-and-other-features-of-optimal-stopping/10.1214/21-EJP733.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "continuous boundary; free boundary problems; Local time; one-dimensional diffusions; Optimal stopping; smooth-fit", } @Article{Das:2022:UTL, author = "Sayan Das and Weitao Zhu", title = "Upper-tail large deviation principle for the {ASEP}", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--34", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP730", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F10; 82C22", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Upper-tail-large-deviation-principle-for-the-ASEP/10.1214/21-EJP730.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "ASEP; Fredholm determinants; large deviations; Lyapunov exponents", } @Article{Salins:2022:GSS, author = "Michael Salins", title = "Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--17", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP740", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 35R60", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Global-solutions-for-the-stochastic-reaction-diffusion-equation-with-super/10.1214/22-EJP740.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Dissipativity; explosion; global solution; Reaction-diffusion", } @Article{Kolesnik:2022:S, author = "Brett Kolesnik", title = "The sharp {$ K_4 $}-percolation threshold on the {Erd{\H{o}}s--R{\'e}nyi} random graph", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--23", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP710", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C80; 60K35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-sharp-K4-percolation-threshold-on-the-Erd%c5%91sR%c3%a9nyi-random-graph/10.1214/21-EJP710.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bootstrap percolation; random graph; triadic closure; weak saturation", } @Article{Busani:2022:NEB, author = "Ofer Busani and Timo Sepp{\"a}l{\"a}inen", title = "Non-existence of bi-infinite polymers", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--40", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP731", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Non-existence-of-bi-infinite-polymers/10.1214/21-EJP731.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Busemann function; Directed polymer; Geodesic; Gibbs measure; inverse-gamma polymer; Kardar-Parisi-Zhang universality; log-gamma polymer; random environment; Random walk", } @Article{Lacker:2022:QAI, author = "Daniel Lacker", title = "Quantitative approximate independence for continuous mean field {Gibbs} measures", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--21", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP743", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B21; 60F05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Quantitative-approximate-independence-for-continuous-mean-field-Gibbs-measures/10.1214/22-EJP743.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Fisher information; Gibbs measures; mean field limit; propagation of chaos; Relative entropy", } @Article{Duquesne:2022:SLT, author = "Thomas Duquesne and Robin Khanfir and Shen Lin and Niccol{\`o} Torri", title = "Scaling limits of tree-valued branching random walks", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--54", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP741", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60G50; 60G52; 60F17", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Scaling-limits-of-tree-valued-branching-random-walks/10.1214/22-EJP741.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "branching random walks; Brownian cactus; Brownian snake; Galton--Watson tree; real tree; Scaling limit; Superprocess", } @Article{Cohen:2022:GTU, author = "Samuel N. Cohen and Tanut Treetanthiploet", title = "{Gittins}' theorem under uncertainty", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--48", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP742", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "93E35; 60G40; 91B32; 91B70", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Gittins-theorem-under-uncertainty/10.1214/22-EJP742.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gittins index; Multi-armed bandits; nonlinear expectation; robustness; time-consistency; uncertainty", } @Article{Greven:2022:SPS, author = "Andreas Greven and Frank den Hollander and Margriet Oomen", title = "Spatial populations with seed-bank: well-posedness, duality and equilibrium", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--88", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP728", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J70; 60K35; 92D25", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Spatial-populations-with-seed-bank--well-posedness-duality-and/10.1214/21-EJP728.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "coexistence versus clustering; Duality; Equilibrium; Fisher-Wright diffusion; migration; Resampling; seed-bank", } @Article{Nakajima:2022:MET, author = "Shuta Nakajima", title = "Maximal edge-traversal time in first-passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP746", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60K35; 82A51; 82D30", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Maximal-edge-traversal-time-in-First-passage-percolation/10.1214/22-EJP746.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "First-passage percolation; maximal edge-traversal time", } @Article{Djete:2022:EMF, author = "Mao Fabrice Djete", title = "Extended mean field control problem: a propagation of chaos result", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--53", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP726", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Extended-mean-field-control-problem--a-propagation-of-chaos/10.1214/21-EJP726.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60-XX; 60Fxx; 60GXX; law of control; McKean--Vlasov process; Mean--Field control; propagation of chaos", } @Article{Melbourne:2022:APM, author = "Ian Melbourne and Dalia Terhesiu", title = "Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--17", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP750", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F10; 37D20; 37A50", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Analytic-proof-of-multivariate-stable-local-large-deviations-and-application/10.1214/22-EJP750.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "local large deviations; multivariate stable laws", } @Article{Park:2022:SHC, author = "Hyunchul Park and Renming Song", title = "Spectral heat content for $ \alpha $-stable processes in {$ C^{1, 1} $} open sets", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--19", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP752", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J76", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Spectral-heat-content-for-%ce%b1-stable-processes-in-C11-open/10.1214/22-EJP752.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "asymptotic behavior; spectral heat content; Stable processes", } @Article{Balazs:2022:HLZ, author = "M{\'a}rton Bal{\'a}zs and Felix Maxey-Hawkins", title = "Hydrodynamic limit of the zero range process on a randomly oriented graph", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--29", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP753", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Hydrodynamic-limit-of-the-zero-range-process-on-a-randomly/10.1214/22-EJP753.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Hydrodynamic limit; random environment; Relative entropy; Zero range process", } @Article{Shcherbina:2022:STM, author = "Tatyana Shcherbina", title = "{SUSY} transfer matrix approach for the real symmetric 1d random band matrices", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--29", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP747", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/SUSY-transfer-matrix-approach-for-the-real-symmetric-1d-random/10.1214/22-EJP747.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "characteristic polynomials; random band matrices; real symmetric case; SUSY; Universality", } @Article{Gravner:2022:ODC, author = "Janko Gravner and Xiaochen Liu", title = "One-dimensional cellular automata with random rules: longest temporal period of a periodic solution", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--23", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP744", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 37B15; 68Q80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/One-dimensional-cellular-automata-with-random-rules--longest-temporal/10.1214/22-EJP744.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian bridge; cellular automaton; periodic solution; random rule", } @Article{Saloff-Coste:2022:RWF, author = "Laurent Saloff-Coste and Yuwen Wang", title = "Random walks on finite nilpotent groups driven by long-jump measures", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--31", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP745", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Random-walks-on-finite-nilpotent-groups-driven-by-long-jump/10.1214/22-EJP745.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "group; mixing time; Random walk", } @Article{Adhikari:2022:SDG, author = "Arka Adhikari", title = "Spin distributions for generic spherical spin glasses", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--43", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP755", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Spin-distributions-for-generic-spherical-spin-glasses/10.1214/22-EJP755.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "invariance principle; spin distributions; Spin glasses", } @Article{He:2022:MCF, author = "Jimmy He", title = "{Markov} chains on finite fields with deterministic jumps", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--17", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP757", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10; 11T23; 05C81", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Markov-chains-on-finite-fields-with-deterministic-jumps/10.1214/22-EJP757.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Cheeger constant; Markov chain; mixing time; spectral gap", } @Article{Cai:2022:NAC, author = "T. Tony Cai and Rungang Han and Anru R. Zhang", title = "On the non-asymptotic concentration of heteroskedastic {Wishart}-type matrix", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--40", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP758", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 46B09", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-the-non-asymptotic-concentration-of-heteroskedastic-Wishart-type-matrix/10.1214/22-EJP758.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "concentration inequality; nonasymptotic bound; Random matrix; Wishart matrix", } @Article{Lehericy:2022:FPP, author = "Thomas Leh{\'e}ricy", title = "First-passage percolation in random planar maps and {Tutte}'s bijection", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--50", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP662", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 05C80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/First-passage-percolation-in-random-planar-maps-and-Tuttes-bijection/10.1214/21-EJP662.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "first passage percolation; Probability; Random maps", } @Article{Collin:2022:REC, author = "Orph{\'e}e Collin and Francis Comets", title = "Rate of escape of conditioned {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--26", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/21-EJP737", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60J60; 60J65; 60G17", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Rate-of-escape-of-conditioned-Brownian-motion/10.1214/21-EJP737.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "autoregressive process; Bessel process; Brownian motion; Conditioning; random difference equation; regeneration; transience; upper-class and lower-class; Wiener moustache", } @Article{Mastrostefano:2022:ASU, author = "Daniele Mastrostefano", title = "An almost sure upper bound for random multiplicative functions on integers with a large prime factor", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--21", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP751", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "11K65; 11N64", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/An-almost-sure-upper-bound-for-random-multiplicative-functions-on/10.1214/22-EJP751.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Borel--Cantelli lemma; Law of iterated logarithm; low moments; random multiplicative functions; Sums of independent random variables", } @Article{Filmus:2022:LSI, author = "Yuval Filmus and Ryan O'Donnell and Xinyu Wu", title = "Log-{Sobolev} inequality for the multislice, with applications", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--30", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP749", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10; 05E18; 68R05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Log-Sobolev-inequality-for-the-multislice-with-applications/10.1214/22-EJP749.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "combinatorics; conductance; Fourier analysis; hypercontractivity; Log-Sobolev inequality; Markov chains; representation theory; small-set expansion", } @Article{Shen:2022:TFI, author = "Jinqi Shen and Stilian Stoev and Tailen Hsing", title = "Tangent fields, intrinsic stationarity, and self similarity", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--56", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP754", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G10; 60G12; 60G18; 60G22; 62R10; 62H11", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Tangent-fields-intrinsic-stationarity-and-self-similarity/10.1214/22-EJP754.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Functional data analysis; IRFk; operator self-similarity; Spectral theory; tangent field", } @Article{Lis:2022:SPH, author = "Marcin Lis", title = "Spins, percolation and height functions", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--21", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP761", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Spins-percolation-and-height-functions/10.1214/22-EJP761.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "height functions; percolation; spin models", } @Article{Can:2022:RCM, author = "Van Hao Can and Khanh Duy Trinh", title = "Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--40", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP759", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60D05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Random-connection-models-in-the-thermodynamic-regime--central-limit/10.1214/22-EJP759.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Betti numbers; central limit theorem; clique complex; random connection model; weak stabilization", } @Article{Galeati:2022:DDS, author = "Lucio Galeati and Fabian A. Harang and Avi Mayorcas", title = "Distribution dependent {SDEs} driven by additive continuous noise", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--38", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP756", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10; 60F15; 60K35; 34F05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Distribution-dependent-SDEs-driven-by-additive-continuous-noise/10.1214/22-EJP756.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Additive Noise; McKean--Vlasov equation; mean field limit; pathwise approach", } @Article{Apollonio:2022:MIM, author = "Valentina Apollonio and Vanessa Jacquier and Francesca Romana Nardi and Alessio Troiani", title = "Metastability for the {Ising} model on the hexagonal lattice", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--48", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP763", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10; 60J45; 82C20; 05B45", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Metastability-for-the-Ising-model-on-the-hexagonal-lattice/10.1214/22-EJP763.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "hexagonal lattice; Ising model; large deviations; low temperature stochastic dynamics; metastability; polyiamonds; potential theory", } @Article{Nassif:2022:ZRS, author = "Michel Nassif", title = "Zooming in at the root of the stable tree", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--38", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP764", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 60G55; 60G52", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Zooming-in-at-the-root-of-the-stable-tree/10.1214/22-EJP764.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Additive functionals; L{\'e}vy trees; Scaling limit", } @Article{Wang:2022:DTP, author = "Zhe Wang", title = "A driven tagged particle in asymmetric exclusion processes", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--46", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP760", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 47A35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/A-driven-tagged-particle-in-asymmetric-exclusion-processes/10.1214/22-EJP760.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Interacting particle system; Invariant measures; Tagged particles", } @Article{Pirogov:2022:CPG, author = "Sergey Pirogov and Elena Zhizhina", title = "Contact processes on general spaces. Models on graphs and on manifolds", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--14", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP765", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82C22; 82B21; 60K35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Contact-processes-on-general-spaces-Models-on-graphs-and-on/10.1214/22-EJP765.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "birth and death process; correlation functions; critical regime; hierarchical equations; infinite particle configurations", } @Article{Spiro:2022:OCG, author = "Sam Spiro", title = "Online card games", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--15", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP768", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Online-card-games/10.1214/22-EJP768.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "card shuffling; Discrete probability; Game theory", } @Article{Bao:2022:EIP, author = "Jianhai Bao and Michael Scheutzow and Chenggui Yuan", title = "Existence of invariant probability measures for functional {McKean--Vlasov} {SDEs}", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--14", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP773", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 47D07", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Existence-of-invariant-probability-measures-for-functional-McKean--Vlasov-SDEs/10.1214/22-EJP773.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "functional McKean--Vlasov SDE; invariant probability measure; Kakutani's fixed point theorem", } @Article{Fleermann:2022:LSL, author = "Michael Fleermann and Werner Kirsch and Thomas Kriecherbauer", title = "Local semicircle law for {Curie--Weiss} type ensembles", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--27", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP767", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Local-semicircle-law-for-Curie-Weiss-type-ensembles/10.1214/22-EJP767.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "correlated entries; Curie-Weiss entries; exchangeable entries; Local semicircle law; Random matrix", } @Article{Parekh:2022:PRW, author = "Shalin Parekh", title = "Positive random walks and an identity for half-space {SPDEs}", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--47", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP775", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 82C23", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Positive-random-walks-and-an-identity-for-half-space-SPDEs/10.1214/22-EJP775.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "anomalous fluctuations; Brownian excursion; Brownian meander; concentration of measure; Directed polymer; Dirichlet boundary; stochastic heat equation with multiplicative noise", } @Article{Guionnet:2022:LDG, author = "Alice Guionnet and Ronan Memin", title = "Large deviations for {Gibbs} ensembles of the classical {Toda} chain", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--29", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP771", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 60K35; 60F10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Large-deviations-for-Gibbs-ensembles-of-the-classical-Toda-chain/10.1214/22-EJP771.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Beta ensembles; empirical measure of eigenvalues; generalized Gibbs ensemble; large deviations; random matrices; Toda chain", } @Article{Janson:2022:CLT, author = "Svante Janson", title = "Central limit theorems for additive functionals and fringe trees in tries", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--63", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP776", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05; 05C05; 68P05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Central-limit-theorems-for-additive-functionals-and-fringe-trees-in/10.1214/22-EJP776.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Additive functionals; asymptotic normality; protected nodes; random tries", } @Article{Liu:2022:AAH, author = "Gi-Ren Liu and Yuan-Chung Sheu and Hau-Tieng Wu", title = "Asymptotic analysis of higher-order scattering transform of {Gaussian} processes", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--27", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP766", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G60; 60H05; 62M15; 35K15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Asymptotic-analysis-of-higher-order-scattering-transform-of-Gaussian-processes/10.1214/22-EJP766.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Malliavin calculus; scaling limits; scattering transform; Stein's method; wavelet transform; Wiener-It{\^o} decomposition", } @Article{Bordenave:2022:NST, author = "Charles Bordenave and Jaehun Lee", title = "Noise sensitivity for the top eigenvector of a sparse random matrix", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--50", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP770", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Noise-sensitivity-for-the-top-eigenvector-of-a-sparse-random/10.1214/22-EJP770.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Noise sensitivity; sparse random matrix", } @Article{Bhattacharya:2022:PHT, author = "Ayan Bhattacharya and Zbigniew Palmowski and Bert Zwart", title = "Persistence of heavy-tailed sample averages: principle of infinitely many big jumps", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--25", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP774", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F99; 60G10; 60G50; 60G18; 60G52; 60K35; 60K40; 60J80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Persistence-of-heavy-tailed-sample-averages--principle-of-infinitely/10.1214/22-EJP774.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "heavy-tailed distribution; large deviation; persistency; Random walk; regular variation", } @Article{Harel:2022:FCR, author = "Matan Harel and Yinon Spinka", title = "Finitary codings for the random-cluster model and other infinite-range monotone models", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP778", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "28D99; 60K35; 82B20; 82B26; 37A60", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Finitary-codings-for-the-random-cluster-model-and-other-infinite/10.1214/22-EJP778.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Coupling from the past; factor of iid; finitary coding; monotone specification; quasi-transitive graph; Random-cluster model", } @Article{Bates:2022:FEM, author = "Erik Bates and Youngtak Sohn", title = "Free energy in multi-species mixed p -spin spherical models", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--75", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP780", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60G15; 82B44; 82D30", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Free-energy-in-multi-species-mixed-p-spin-spherical-models/10.1214/22-EJP780.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Aizenman--Sims--Starr scheme; Cavity method; Free energy; Guerra interpolation; multi-species spin glass; Parisi formula; spherical spin glass; synchronization", } @Article{Enriquez:2022:DFE, author = "Nathana{\"e}l Enriquez and Gabriel Faraud and Laurent M{\'e}nard and Nathan Noiry", title = "Depth first exploration of a configuration model", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--27", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP762", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82C21; 60J20; 60F10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Depth-first-exploration-of-a-configuration-model/10.1214/22-EJP762.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "configuration model; depth first search algorithm; differential equation method", } @Article{Ambrosio:2022:QRM, author = "Luigi Ambrosio and Michael Goldman and Dario Trevisan", title = "On the quadratic random matching problem in two-dimensional domains", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--35", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP784", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 90C05; 60F25; 35J05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-the-quadratic-random-matching-problem-in-two-dimensional-domains/10.1214/22-EJP784.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "39B62; geometric probability; Matching problem; Optimal transport", } @Article{Peng:2022:WPS, author = "Xuhui Peng and Juan Yang and Jianliang Zhai", title = "Well-posedness of stochastic {$2$D} hydrodynamics type systems with multiplicative {L{\'e}vy} noises", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--31", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP779", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60H07", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Well-posedness-of-stochastic-2D-hydrodynamics-type-systems-with-multiplicative/10.1214/22-EJP779.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "cutting off argument; multiplicative L{\'e}vy noise; stochastic 2D hydrodynamics type systems", } @Article{Can:2022:SDS, author = "V. H. Can and D. A. Croydon and T. Kumagai", title = "Spectral dimension of simple random walk on a long-range percolation cluster", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--37", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP783", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 35K05; 60J15; 60J35; 60J74; 82B43", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Spectral-dimension-of-simple-random-walk-on-a-long-range/10.1214/22-EJP783.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Heat kernel estimates; Long-range percolation; Random walk; Spectral dimension", } @Article{Ouaki:2022:MSC, author = "Mehdi Ouaki and Jim Pitman", title = "{Markovian} structure in the concave majorant of {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--21", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP769", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51; 60G55; 60J65", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Markovian-structure-in-the-concave-majorant-of-Brownian-motion/10.1214/22-EJP769.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian motion; convex minorant; Path decomposition", } @Article{Gangopadhyay:2022:FTI, author = "Ujan Gangopadhyay", title = "Fluctuations of transverse increments in two-dimensional first passage percolation", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--61", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP772", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82B43", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Fluctuations-of-transverse-increments-in-two-dimensional-first-passage-percolation/10.1214/22-EJP772.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "first passage percolation; fluctuation exponent; transverse increments; wandering exponent", } @Article{Ramil:2022:QSD, author = "Mouad Ramil", title = "Quasi-stationary distribution for the {Langevin} process in cylindrical domains, part {II}: overdamped limit", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--18", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP789", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82C31; 35B25; 47B07; 60H10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Quasi-stationary-distribution-for-the-Langevin-process-in-cylindrical-domains/10.1214/22-EJP789.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Langevin process; overdamped Langevin process; overdamped limit; quasi-stationary distribution", } @Article{Gracar:2022:RVT, author = "Peter Gracar and Markus Heydenreich and Christian M{\"o}nch and Peter M{\"o}rters", title = "Recurrence versus transience for weight-dependent random connection models", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--31", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP748", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 05C80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Recurrence-versus-transience-for-weight-dependent-random-connection-models/10.1214/22-EJP748.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Boolean model; preferential attachment; random-connection model; recurrence; Scale-free percolation; transience", } @Article{Bally:2022:UMA, author = "Vlad Bally and Lucia Caramellino and Arturo Kohatsu-Higa", title = "Using moment approximations to study the density of jump driven {SDEs}", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--21", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP785", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G51; 60H07; 60H20; 44A60", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Using-moment-approximations-to-study-the-density-of-jump-driven/10.1214/22-EJP785.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Interpolation method; L{\'e}vy driven sde's; Moment problem; Smoothness of densities", } @Article{Gusakova:2022:TDT, author = "Anna Gusakova and Zakhar Kabluchko and Christoph Th{\"a}le", title = "The {\textbeta} -Delaunay tessellation {II}: the {Gaussian} limit tessellation", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--33", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP782", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "52A22; 52B11; 53C65; 60D05; 60F05; 60F17; 60G55", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-%ce%b2-Delaunay-tessellation-II-the-Gaussian-limit-tessellation/10.1214/22-EJP782.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "angle sums; beta'-Delaunay tessellation; beta-Delaunay tessellation; Gaussian simplex; Gaussian-Delaunay tessellation; Laguerre tessellation; paraboloid convexity; paraboloid hull process; Poisson point process; Stochastic geometry; typical cell; weighted typical cell", } @Article{Oviedo:2022:SOC, author = "Giancarlos Oviedo and Gonzalo Panizo and Alejandro F. Ram{\'\i}rez", title = "Second order cubic corrections of large deviations for perturbed random walks", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--45", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP786", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 82D30; 82C23; 82C41", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Second-order-cubic-corrections-of-large-deviations-for-perturbed-random/10.1214/22-EJP786.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "beta random walk; GUE Tracy-Widom distribution; Random walk in random environment", } @Article{Bladt:2022:TMR, author = "Martin Bladt and Enkelejd Hashorva and Georgiy Shevchenko", title = "Tail measures and regular variation", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--43", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP788", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "28A33; 60G70", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Tail-measures-and-regular-variation/10.1214/22-EJP788.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "c{\`a}dl{\`a}g processes; hidden regular variation; max-stable processes; regular variation; spectral tail processes; tail measures; tail processes; weak convergence", } @Article{Kaleta:2022:DCE, author = "Kamil Kaleta and Daniel Ponikowski", title = "On directional convolution equivalent densities", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--19", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP790", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60E05; 60G50; 60G51; 26B99; 62H05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-directional-convolution-equivalent-densities/10.1214/22-EJP790.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "almost radial decreasing function; Compound Poisson measure; cone; Exponential decay; infinitely divisible distribution; isotropic unimodal distribution; L{\'e}vy process; multivariate density; random sum; spatial asymptotics; subexponential distribution", } @Article{Bosi:2022:RWT, author = "Gianluca Bosi and Yiping Hu and Yuval Peres", title = "Recurrence and windings of two revolving random walks", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--22", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP781", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 60J10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Recurrence-and-windings-of-two-revolving-random-walks/10.1214/22-EJP781.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Lyapunov function; oriented lattices; transience/recurrence; winding", } @Article{Avena:2022:LEP, author = "Luca Avena and Alexandre Gaudilli{\`e}re and Paolo Milanesi and Matteo Quattropani", title = "Loop-erased partitioning of a graph: mean-field analysis", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--35", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP792", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C81; 05C85; 60J10; 60J27; 60J28", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Loop-erased-partitioning-of-a-graph-mean-field-analysis/10.1214/22-EJP792.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "discrete Laplacian; Loop-erased random walk; Random partitions; spanning rooted forests; Wilson's algorithm", } @Article{Bowditch:2022:BRW, author = "Adam M. Bowditch and David A. Croydon", title = "Biased random walk on supercritical percolation: anomalous fluctuations in the ballistic regime", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--22", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP794", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60G50; 60K35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Biased-random-walk-on-supercritical-percolation--anomalous-fluctuations-in/10.1214/22-EJP794.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "biased random walk; Random walk in random environment; Supercritical percolation; trapping", } @Article{Lauriere:2022:BPC, author = "Mathieu Lauri{\`e}re and Ludovic Tangpi", title = "Backward propagation of chaos", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--30", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP777", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "35K58; 35B40; 60F25; 60J60; 28C20; 60H20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Backward-propagation-of-chaos/10.1214/22-EJP777.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "BSDE; concentration of measure; interacting particles systems; McKean--Vlasov BSDE; PDEs on Wasserstein space; propagation of chaos", } @Article{Dominguez:2022:GGP, author = "Tomas Dominguez", title = "The $ \ell^p $ {Gaussian--Grothendieck} problem with vector spins", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--46", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP801", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82D30; 82B44; 60K35; 60G15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-%e2%84%93p-Gaussian-Grothendieck-problem-with-vector-spins/10.1214/22-EJP801.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Ground state energy; Parisi formula; Spin glasses; vector spins", } @Article{Privault:2022:BEB, author = "Nicolas Privault and Grzegorz Serafin", title = "{Berry--Esseen} bounds for functionals of independent random variables", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--37", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP795", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60G57; 60H07", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Berry--Esseen-bounds-for-functionals-of-independent-random-variables/10.1214/22-EJP795.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Berry--Esseen bounds; Kolmogorov distance; Malliavin calculus; Quadratic forms; Stein-Chen method; U-statistics", } @Article{Li:2022:DBM, author = "Liping Li and Shuwen Lou", title = "Distorted {Brownian} motions on space with varying dimension", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP796", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J45; 60J46; 60J60; 60J65", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Distorted-Brownian-motions-on-space-with-varying-dimension/10.1214/22-EJP796.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Dirichlet forms; distorted Brownian motions; Heat kernel estimates; varying dimension", } @Article{Hinz:2022:SRO, author = "Michael Hinz and Jonas M. T{\"o}lle and Lauri Viitasaari", title = "{Sobolev} regularity of occupation measures and paths, variability and compositions", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--29", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP797", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "26B30; 46E35; 60G17; 60G22; 60G51; 26A33; 31B15; 42B20; 42B35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Sobolev-regularity-of-occupation-measures-and-paths-variability-and-compositions/10.1214/22-EJP797.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "compositions; fractional Sobolev regularity; Functions of bounded variation; Local times; occupation measures", } @Article{Husson:2022:LDL, author = "Jonathan Husson", title = "Large deviations for the largest eigenvalue of matrices with variance profiles", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--44", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP793", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 60F10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Large-deviations-for-the-largest-eigenvalue-of-matrices-with-variance/10.1214/22-EJP793.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "large deviations; Largest eigenvalue; random matrices", } @Article{Ho:2022:EAB, author = "Fu-Hsuan Ho and Pascal Maillard", title = "Efficient approximation of branching random walk {Gibbs} measures", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--18", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP800", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "68Q17; 82D30; 60K35; 60J80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Efficient-approximation-of-branching-random-walk-Gibbs-measures/10.1214/22-EJP800.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "algorithmic hardness; Branching random walk; Gibbs measure; Kullback--Leibler divergence; sampling algorithm", } @Article{Fountoulakis:2022:CPP, author = "Nikolaos Fountoulakis and Tejas Iyer", title = "Condensation phenomena in preferential attachment trees with neighbourhood influence", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--49", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP787", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "90B15; 60J20; 05C80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Condensation-phenomena-in-preferential-attachment-trees-with-neighbourhood-influence/10.1214/22-EJP787.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "preferential attachment trees; P{\'o}lya processes; Random recursive trees; scale-free", } @Article{Scoppola:2022:SDC, author = "Benedetto Scoppola and Alessio Troiani and Matteo Veglianti", title = "Shaken dynamics on the 3d cubic lattice", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--26", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP803", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B20; 82B26; 82B27; 82C20; 82C27; 60J10; 60J22", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Shaken-dynamics-on-the-3d-cubic-lattice/10.1214/22-EJP803.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Ising model; numerical simulations; parallel dynamics; Phase transitions; Probabilistic cellular automata", } @Article{Grimmett:2022:BSR, author = "Geoffrey R. Grimmett and Zhongyang Li", title = "{Brownian} snails with removal: epidemics in diffusing populations", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--31", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP804", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60G15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Brownian-snails-with-removal-epidemics-in-diffusing-populations/10.1214/22-EJP804.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "diffusion; Epidemic; frog model; infectious disease; percolation; SIR model; snail model; Wiener sausage", } @Article{Betken:2022:VAC, author = "Carina Betken and Matthias Schulte and Christoph Th{\"a}le", title = "Variance asymptotics and central limit theory for geometric functionals of {Poisson} cylinder processes", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--47", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP805", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 52A22; 53C65; 60F05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Variance-asymptotics-and-central-limit-theory-for-geometric-functionals-of/10.1214/22-EJP805.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Berry--Esseen bound; central limit theorem; geometric functional; intrinsic volume; multivariate central limit theorem; Poisson cylinder process; second-order Poincar{\'e} inequality; Stochastic geometry; variance asymptotics", } @Article{Lata:2022:NRC, author = "Rafa{\l} Lata and Witold {\'S}wi{\k{a}}tkowski", title = "Norms of randomized circulant matrices", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--23", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP799", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 15B20; 46B09", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Norms-of-randomized-circulant-matrices/10.1214/22-EJP799.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Circulant matrix; non-homogeneous random matrix; operator norm", } @Article{Caravenna:2022:GLS, author = "Francesco Caravenna and Francesca Cottini", title = "{Gaussian} limits for subcritical chaos", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--35", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP798", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 82B44; 35R60", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Gaussian-limits-for-subcritical-chaos/10.1214/22-EJP798.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; Directed polymer in random environment; Edwards-Wilkinson fluctuations; KPZ equation; polynomial chaos; Stochastic heat equation; Wiener Chaos", } @Article{Kesten:2022:OPR, author = "Harry Kesten and Vladas Sidoravicius and Maria Eul{\'a}lia Vares", title = "Oriented percolation in a random environment", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--49", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP791", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82B43", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Oriented-percolation-in-a-random-environment/10.1214/22-EJP791.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Oriented percolation; random environment", } @Article{Lubinsky:2022:VRZ, author = "Doron S. Lubinsky and Igor E. Pritsker", title = "Variance of real zeros of random orthogonal polynomials for varying and exponential weights", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP802", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G15; 42C05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Variance-of-real-zeros-of-random-orthogonal-polynomials-for-varying/10.1214/22-EJP802.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Exponential weights; Random orthogonal polynomials; variance of real zeros", } @Article{Bahl:2022:DLA, author = "Riti Bahl and Philip Barnet and Tobias Johnson and Matthew Junge", title = "Diffusion-limited annihilating systems and the increasing convex order", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--19", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP808", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60J80; 60J10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Diffusion-limited-annihilating-systems-and-the-increasing-convex-order/10.1214/22-EJP808.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Interacting particle system; stochastic order", } @Article{Foxall:2022:FTR, author = "Eric Foxall and Bilal Madani and Adam Roemer", title = "Fixation time of the rock-paper-scissors model: rigorous results in the well-mixed setting", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--23", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP807", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 92D55", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Fixation-time-of-the-rock-paper-scissors-model--rigorous/10.1214/22-EJP807.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "density-dependent Markov chain; diffusion limit; heteroclinic cycle; rock-paper-scissors model; stochastic averaging", } @Article{Yang:2022:LDS, author = "Fan Yang", title = "Limiting distribution of the sample canonical correlation coefficients of high-dimensional random vectors", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--71", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP814", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 62E20; 62H99", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Limiting-distribution-of-the-sample-canonical-correlation-coefficients-of-high/10.1214/22-EJP814.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "BBP transition; canonical correlation analysis; CLT; spiked eigenvalues", } @Article{Pinsky:2022:CCN, author = "Ross G. Pinsky", title = "Clustering of consecutive numbers in permutations under {Mallows} distributions and super-clustering under general $p$-shifted distributions", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--20", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP812", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05; 05A05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Clustering-of-consecutive-numbers-in-permutations-under-Mallows-distributions-and/10.1214/22-EJP812.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "backward ranks; clustering; inversion; Mallows distribution; p-shifted; random permutation; Runs", } @Article{Cardona:2022:RDS, author = "Jorge Cardona and Martina Hofmanov{\'a} and Torstein Nilssen and Nimit Rana", title = "Random dynamical system generated by the {$3$D} {Navier--Stokes} equation with rough transport noise", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--27", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP813", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60L20; 60L50; 35Q30; 37H10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Random-dynamical-system-generated-by-the-3D-Navier--Stokes-equation/10.1214/22-EJP813.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Navier--Stokes equations; Random dynamical system; Rough paths", } @Article{Velicu:2022:LSI, author = "Andrei Velicu", title = "Logarithmic {Sobolev} inequalities for {Dunkl} operators with applications to functional inequalities for singular {Boltzmann--Gibbs} measures", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--25", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP810", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60E15; 35A23; 26D10; 46N55; 42B10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Logarithmic-Sobolev-inequalities-for-Dunkl-operators-with-applications-to-functional/10.1214/22-EJP810.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "43A32; Boltzmann-Gibbs measure; concentration of measure; Dunkl operators; Logarithmic Sobolev inequality; Poincar{\'e} inequality", } @Article{Couronne:2022:EPS, author = "Olivier Couronn{\'e}", title = "Entanglement percolation and spheres in", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--17", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP816", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Entanglement-percolation-and-spheres-in-Zd/10.1214/22-EJP816.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Entanglement percolation; percolation; random sphere", } @Article{Hilario:2022:RCP, author = "Marcelo Hil{\'a}rio and Daniel Ungaretti and Daniel Valesin and Maria Eul{\'a}lia Vares", title = "Results on the contact process with dynamic edges or under renewals", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--31", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP811", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K05; 82B43", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Results-on-the-contact-process-with-dynamic-edges-or-under/10.1214/22-EJP811.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "contact process; percolation; random environment; Renewal process", } @Article{Collevecchio:2022:LTE, author = "Andrea Collevecchio and Kais Hamza and Meng Shi and Ruth J. Williams", title = "Limit theorems and ergodicity for general bootstrap random walks", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--22", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP818", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 60F17; 28D05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Limit-theorems-and-ergodicity-for-general-bootstrap-random-walks/10.1214/22-EJP818.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "ergodicity; Functional limit theorems; long memory; L{\'e}vy transformation; Random walks", } @Article{Penington:2022:GSD, author = "Sarah Penington and Matthew I. Roberts and Zs{\'o}fia Talyig{\'a}s", title = "Genealogy and spatial distribution of the {$N$}-particle branching random walk with polynomial tails", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--65", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP806", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60J80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Genealogy-and-spatial-distribution-of-the-N-particle-branching-random/10.1214/22-EJP806.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Branching random walk; genealogy; heavy-tailed distribution; selection; star-shaped coalescent", } @Article{Heiny:2022:LSC, author = "Johannes Heiny", title = "Large sample correlation matrices: a comparison theorem and its applications", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--20", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP817", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G10; 60G57; 60G70", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Large-sample-correlation-matrices--a-comparison-theorem-and-its/10.1214/22-EJP817.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Largest eigenvalue; Limiting spectral distribution; Primary 60B20; sample correlation matrix; secondary 60F05; smallest eigenvalue", } @Article{Bertacco:2022:RSP, author = "Federico Bertacco and Carlo Orrieri and Luca Scarpa", title = "Random separation property for stochastic {Allen--Cahn}-type equations", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP830", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "35K10; 35K55; 35K67; 60H15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Random-separation-property-for-stochastic-Allen--Cahn-type-equations/10.1214/22-EJP830.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "exponential estimates; Logarithmic potential; random separation property; stochastic Allen--Cahn equation", } @Article{Butelmann:2022:SLS, author = "Ian Butelmann and Gregorio R. Moreno Flores", title = "Scaling limit of stationary coupled {Sasamoto--Spohn} models", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--25", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP819", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60L50", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Scaling-limit-of-stationary-coupled-Sasamoto-Spohn-models/10.1214/22-EJP819.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "coupled Burgers equations; energy solutions; Interacting diffusions; KPZ equation", } @Article{Cai:2022:CUP, author = "Zhenhao Cai and Eviatar B. Procaccia and Yuan Zhang", title = "Continuity and uniqueness of percolation critical parameters in finitary random interlacements", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--46", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP824", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60G55; 60D05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Continuity-and-uniqueness-of-percolation-critical-parameters-in-finitary-random/10.1214/22-EJP824.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "critical parameteres; finitary random interlacements; percolation", } @Article{Cygan:2022:CHS, author = "Wojciech Cygan and Nikola Sandri{\'c} and Stjepan {\v{S}}ebek", title = "Convex hulls of stable random walks", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--30", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP826", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 60D05; 60F05; 60G52", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Convex-hulls-of-stable-random-walks/10.1214/22-EJP826.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Convex hull; domain of attraction; intrinsic volume; Random walk; Stable law", } @Article{Lou:2022:DAB, author = "Shuwen Lou", title = "Discrete approximation to {Brownian} motion with varying dimension in unbounded domains", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--33", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP829", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J35; 60J65", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Discrete-approximation-to-Brownian-motion-with-varying-dimension-in-unbounded/10.1214/22-EJP829.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian motion; Dirichlet forms; Heat kernel estimates; Isoperimetric inequality; Nash-type inequality; Primary 60J27; Random walk; Secondary 31C25; Skorokhod space; Space of varying dimension; tightness", } @Article{Ott:2022:EPC, author = "S{\'e}bastien Ott", title = "Existence and properties of connections decay rate for high temperature percolation models", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--19", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP822", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82B43", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Existence-and-properties-of-connections-decay-rate-for-high-temperature/10.1214/22-EJP822.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "asymptotics; convexity; correlation length; decay rate; high-temperature; Mixing; percolation", } @Article{Tough:2022:FVP, author = "Oliver Tough and James Nolen", title = "The {Fleming--Viot} process with {McKean--Vlasov} dynamics", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--72", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP820", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60J80; 60H10; 35K55; 35Q84; 82C22", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-Fleming-Viot-process-with-McKean--Vlasov-dynamics/10.1214/22-EJP820.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Fleming-Viot processes; McKean--Vlasov processes; Quasi-stationary distributions", } @Article{Collins:2022:SDS, author = "Beno{\^\i}t Collins and Jianfeng Yao and Wangjun Yuan", title = "On spectral distribution of sample covariance matrices from large dimensional and large $k$-fold tensor products", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--18", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP825", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-spectral-distribution-of-sample-covariance-matrices-from-large-dimensional/10.1214/22-EJP825.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "eigenvalue distribution; large k-fold tensors; Mar{\v{c}}enko-Pastur law; Primary 60B20; quantum information theory; Secondary 15B52", } @Article{Bhamidi:2022:GLM, author = "Shankar Bhamidi and Souvik Dhara and Remco van der Hofstad and Sanchayan Sen", title = "Global lower mass-bound for critical configuration models in the heavy-tailed regime", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--29", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP821", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05; 05C80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Global-lower-mass-bound-for-critical-configuration-models-in-the/10.1214/22-EJP821.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Critical configuration model; global lower mass-bound; heavy-tailed degrees", } @Article{Bahlali:2022:ADS, author = "Khaled Bahlali and Brahim Boufoussi and Soufiane Mouchtabih", title = "Approximation of a degenerate semilinear {PDE} with a nonlinear {Neumann} boundary condition", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--21", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP823", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H99; 60H30; 35K61", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Approximation-of-a-degenerate-semilinear-PDE-with-a-nonlinear-Neumann/10.1214/22-EJP823.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Backward stochastic differential equations; penalization method; Reflecting stochastic differential equation; viscosity solution", } @Article{Zhu:2022:DND, author = "Theodore Zhu", title = "The distribution of the number of distinct values in a finite exchangeable sequence", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--25", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP815", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G09; 60C05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-distribution-of-the-number-of-distinct-values-in-a/10.1214/22-EJP815.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Ewens-Pitman two-parameter family; exchangeable random partitions; exchangeable sequences; occupancy problem", } @Article{Forien:2022:SPD, author = "Rapha{\"e}l Forien", title = "Stochastic partial differential equations describing neutral genetic diversity under short range and long range dispersal", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--41", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP827", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17; 60G60; 60J90; 60G52; 92D15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Stochastic-partial-differential-equations-describing-neutral-genetic-diversity-under-short/10.1214/22-EJP827.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; isolation by distance; Lambda-Fleming-Viot processes; long range dispersal; Measure-valued processes; neutral markers; Spatial coalescent", } @Article{Bencs:2022:AMM, author = "Ferenc Bencs and Andr{\'a}s M{\'e}sz{\'a}ros", title = "Atoms of the matching measure", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--38", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP809", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C31; 05C50; 05C70; 60C05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Atoms-of-the-matching-measure/10.1214/22-EJP809.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "matching measure; matching polynomial; Random operators; unimodular network", } @Article{Soloveychik:2022:LDC, author = "Ilya Soloveychik and Vahid Tarokh", title = "Large deviations of convex polyominoes", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--19", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP835", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05A16; 05B50; 05E10; 60F10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Large-deviations-of-convex-polyominoes/10.1214/22-EJP835.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "convex polyominoes; large deviation principle; pattern recognition; Young diagrams", } @Article{Chatterjee:2022:EAK, author = "Shirshendu Chatterjee and David Sivakoff and Matthew Wascher", title = "The effect of avoiding known infected neighbors on the persistence of a recurring infection process", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--40", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP836", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-effect-of-avoiding-known-infected-neighbors-on-the-persistence/10.1214/22-EJP836.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "contact process; epidemics on networks; evolving networks; SIS epidemic", } @Article{Durrett:2022:SIE, author = "Rick Durrett and Dong Yao", title = "Susceptible--infected epidemics on evolving graphs", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--66", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP828", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J27", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Susceptibleinfected-epidemics-on-evolving-graphs/10.1214/22-EJP828.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "configuration model; phase transition; susceptible--infected model", } @Article{Bhattacharjee:2022:GAS, author = "Chinmoy Bhattacharjee and Ilya Molchanov", title = "{Gaussian} approximation for sums of region-stabilizing scores", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--27", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP832", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60D05; 60G55", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Gaussian-approximation-for-sums-of-region-stabilizing-scores/10.1214/22-EJP832.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; minimal points; Poisson process; stabilization; Stein's method", } @Article{Erhard:2022:WUD, author = "Dirk Erhard and Weijun Xu", title = "Weak universality of dynamical {$ \Phi_3^4 $}: polynomial potential and general smoothing mechanism", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--43", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP833", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Weak-universality-of-dynamical-%ce%a634--polynomial-potential-and-general/10.1214/22-EJP833.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "dynamical {\textPhi}34; general smoothing mechanism; Weak universality", } @Article{Gall:2022:VMB, author = "Jean-Fran{\c{c}}ois Le Gall", title = "The volume measure of the {Brownian} sphere is a {Hausdorff} measure", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--28", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP837", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60D05; 60G17", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-volume-measure-of-the-Brownian-sphere-is-a-Hausdorff/10.1214/22-EJP837.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian sphere; Hausdorff measure; moments of ball volumes; Volume measure", } @Article{Fill:2022:SPS, author = "James Allen Fill and Svante Janson", title = "The sum of powers of subtree sizes for conditioned {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--77", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP831", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C05; 60F05; 60C05; 30E99", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-sum-of-powers-of-subtree-sizes-for-conditioned-GaltonWatson/10.1214/22-EJP831.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "additive functional; Brownian excursion; conditioned Galton--Watson tree; generating function; Hadamard product of sequences; method of moments; polylogarithm; Random analytic function; simply generated random tree; Singularity analysis; subtree sizes; tree recurrence", } @Article{Bobkov:2022:UBF, author = "Sergey G. Bobkov", title = "Upper Bounds for {Fisher} information", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--44", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP834", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Upper-Bounds-for-Fisher-information/10.1214/22-EJP834.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60E; 60FEJP; Fisher information; Sobolev Spaces", } @Article{Bonnefont:2022:ODT, author = "Benjamin Bonnefont", title = "The overlap distribution at two temperatures for the branching {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--21", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP841", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J80; 82D30; 60G70", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-overlap-distribution-at-two-temperatures-for-the-branching-Brownian/10.1214/22-EJP841.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Branching Brownian motion; Gibbs measure; overlap distribution; random energy model", } @Article{Cipolloni:2022:OMR, author = "Giorgio Cipolloni and L{\'a}szl{\'o} Erd{\H{o}}s and Dominik Schr{\"o}der", title = "Optimal multi-resolvent local laws for {Wigner} matrices", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--38", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP838", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20; 15B52", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Optimal-multi-resolvent-local-laws-for-Wigner-matrices/10.1214/22-EJP838.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "global law; Local law; random matrices", } @Article{Addario-Berry:2022:UHW, author = "Louigi Addario-Berry and Anna Brandenberger and Jad Hamdan and C{\'e}line Kerriou", title = "Universal height and width bounds for random trees", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--24", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP842", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05; 60J80; 05C05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Universal-height-and-width-bounds-for-random-trees/10.1214/22-EJP842.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bienaym{\'e} trees; Galton--Watson trees; Height; Random trees; Simply generated trees; width", } @Article{Bogso:2022:PPU, author = "Antoine-Marie Bogso and Moustapha Dieye and Olivier Menoukeu Pamen", title = "Path-by-path uniqueness of multidimensional {SDE's} on the plane with nondecreasing coefficients", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--26", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP844", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H50; 60H10; 60H15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Path-by-path-uniqueness-of-multidimensional-SDEs-on-the-plane/10.1214/22-EJP844.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian sheet; Path-by-path uniqueness; SDEs on the plane; stochastic wave equations", } @Article{Nualart:2022:QCL, author = "David Nualart and Panqiu Xia and Guangqu Zheng", title = "Quantitative central limit theorems for the parabolic {Anderson} model driven by colored noises", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--43", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP847", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60H15; 60H07", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Quantitative-central-limit-theorems-for-the-parabolic-Anderson-model-driven/10.1214/22-EJP847.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Dalang's condition; fractional Brownian motion; Mallivain calculus; Parabolic Anderson model; Quantitative Central Limit Theorem; second-order Poincar{\'e} inequality; Skorohod integral; Stein method", } @Article{Etheridge:2022:GBW, author = "Alison Etheridge and Sarah Penington", title = "Genealogies in bistable waves", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--99", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP845", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J90; 92D10; 60J27", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Genealogies-in-bistable-waves/10.1214/22-EJP845.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Coalescent process; selection; Travelling wave", } @Article{Deya:2022:FDR, author = "Aur{\'e}lien Deya and Renaud Marty", title = "A full discretization of the rough fractional linear heat equation", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--41", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP839", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60G22; 60H35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/A-full-discretization-of-the-rough-fractional-linear-heat-equation/10.1214/22-EJP839.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Fractional noise; space-time discretization procedure; Stochastic heat equation", } @Article{Ho:2022:BMS, author = "Ching-Wei Ho", title = "The {Brown} measure of the sum of a self-adjoint element and an elliptic element", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP840", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "46L54; 60B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-Brown-measure-of-the-sum-of-a-self-adjoint/10.1214/22-EJP840.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brown measure; elliptic element; Non-Hermitian random matrix", } @Article{Guillin:2022:CRV, author = "Arnaud Guillin and Pierre Le Bris and Pierre Monmarch{\'e}", title = "Convergence rates for the {Vlasov--Fokker--Planck} equation and uniform in time propagation of chaos in non convex cases", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--44", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP853", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 35K58; 82B40", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Convergence-rates-for-the-Vlasov-Fokker--Planck-equation-and-uniform/10.1214/22-EJP853.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Coupling method; long-time convergence; propagation of chaos; Vlasov-Fokker--Planck equation", } @Article{Campbell:2022:SHT, author = "Andrew Campbell and Sean O'Rourke", title = "Spectrum of heavy-tailed elliptic random matrices", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--56", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP849", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Spectrum-of-heavy-tailed-elliptic-random-matrices/10.1214/22-EJP849.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "elliptic law; ellitpic random matrices; empirical spectral measure; heavy-tailed entries; Poisson point process; singular values: least singular value; {\textalpha}-stable laws", } @Article{Lachieze-Rey:2022:DGE, author = "Rapha{\"e}l Lachi{\`e}ze-Rey", title = "{Diophantine} {Gaussian} excursions and random walks", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--33", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP854", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G15; 60G50; 11J13; 34L20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Diophantine-Gaussian-excursions-and-random-walks/10.1214/22-EJP854.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "diophantine approximation; Gaussian fields; Gaussian random waves; hyperuniformity; nodal excursion; Random walk; variance cancellation", } @Article{Bruckerhoff:2022:SMS, author = "Martin Br{\"u}ckerhoff and Martin Huesmann and Nicolas Juillet", title = "Shadow martingales --- a stochastic mass transport approach to the peacock problem", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--62", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP846", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G07; 60G44; 60E15; 49Q25; 91G20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Shadow-martingales--a-stochastic-mass-transport-approach-to-the/10.1214/22-EJP846.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Choquet representation; Convex ordering; Kellerer's theorem; Martingale optimal transport; Optimal transport; PCOC; predictable representation property; shadows", } @Article{Chong:2022:ESH, author = "Carsten Chong and P{\'e}ter Kevei", title = "Extremes of the stochastic heat equation with additive {L{\'e}vy} noise", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--21", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP855", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H15; 60F15; 60G70; 60G17; 60G51", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Extremes-of-the-stochastic-heat-equation-with-additive-L%c3%a9vy-noise/10.1214/22-EJP855.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "almost-sure asymptotics; Integral test; Poisson noise; regular variation; stable noise; Stochastic pde", } @Article{Bisewski:2022:DSF, author = "Krzysztof Bisewski and Krzysztof D{\c{e}}bicki and Tomasz Rolski", title = "Derivatives of sup-functionals of fractional {Brownian} motion evaluated at {$ H = 1 / 2 $}", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--35", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP848", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G17; 60G22; 60G70", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Derivatives-of-sup-functionals-of-fractional-Brownian-motion-evaluated-at/10.1214/22-EJP848.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "expected workload; fractional Brownian motion; Pickands constant; Piterbarg constant; Wills functional", } @Article{Garino:2022:AED, author = "Valentin Garino and Ivan Nourdin and Pierre Vallois", title = "Asymptotic error distribution for the {Riemann} approximation of integrals driven by fractional {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--43", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP852", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H05; 60H07; 60F05; 60G15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Asymptotic-error-distribution-for-the-Riemann-approximation-of-integrals-driven/10.1214/22-EJP852.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "fractional Brownian motion; Malliavin-Stein approach; Riemann sum; Rosenblatt process", } @Article{Chiarini:2022:ETE, author = "Alberto Chiarini and Giovanni Conforti and Giacomo Greco and Zhenjie Ren", title = "Entropic turnpike estimates for the kinetic {Schr{\"o}dinger} problem", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP850", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "93E20; 47D07; 60E15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Entropic-turnpike-estimates-for-the-kinetic-Schr%c3%b6dinger-problem/10.1214/22-EJP850.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Schr{\"o}dinger problem; Langevin dynamics; long-time behavior of entropic cost; turnpike estimates; Gamma calculus", } @Article{Guo:2022:QHB, author = "Xiaoqin Guo and Jonathon Peterson and Hung V. Tran", title = "Quantitative homogenization in a balanced random environment", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--31", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP851", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "35J15; 35J25; 35K10; 35K20; 60G50; 60K37; 74Q20; 76M50", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Quantitative-homogenization-in-a-balanced-random-environment/10.1214/22-EJP851.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Berry--Esseen type estimate; non-divergence form difference operators; quantitative stochastic homogenization; Quenched central limit theorem; random walk in a balanced random environment", } @Article{He:2022:MTF, author = "Jimmy He and Huy Tuan Pham and Max Wenqiang Xu", title = "Mixing time of fractional random walk on finite fields", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--15", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP858", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10; 11T23; 05C81", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Mixing-time-of-fractional-random-walk-on-finite-fields/10.1214/22-EJP858.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "finite field; Mixing times; spectral gap", } @Article{Zhang:2022:BEB, author = "Zhuo-Song Zhang", title = "{Berry--Esseen} bounds for generalized {$U$}-statistics", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--36", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP860", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60K35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/BerryEsseen-bounds-for-generalized-U-statistics/10.1214/22-EJP860.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "generalized U-statistics; Stein's method; exchangeable pair approach; Berry--Esseen bound; graphon-generated random graph; Erd{\"o}s-R{\'e}nyi model", } @Article{Baldasso:2022:LSS, author = "Rangel Baldasso and Alexandre Stauffer", title = "Local survival of spread of infection among biased random walks", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--28", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP861", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60K35; 82C22", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Local-survival-of-spread-of-infection-among-biased-random-walks/10.1214/22-EJP861.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "biased random walks; infection processes; interacting particle systems", } @Article{Tang:2022:RPN, author = "Pengfei Tang", title = "Return probabilities on nonunimodular transitive graphs", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--27", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP859", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C81; 60J10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Return-probabilities-on-nonunimodular-transitive-graphs/10.1214/22-EJP859.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "first return probability; nonunimodular transitive graphs; return probability", } @Article{Durhuus:2022:TPL, author = "Bergfinnur Durhuus and Meltem {\"U}nel", title = "Trees with power-like height dependent weight", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--24", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP857", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B10; 05C05; 60J80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Trees-with-power-like-height-dependent-weight/10.1214/22-EJP857.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "height coupled trees; local limits of BGW trees; Random trees", } @Article{Englander:2022:CRW, author = "J{\'a}nos Engl{\"a}nder and Stanislav Volkov", title = "Conservative random walk", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--29", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP863", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 60F05; 60J10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Conservative-random-walk/10.1214/22-EJP863.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "coin-turning; conservative random walk; cooling dynamics; correlated random walk; heating dynamics; invariance principle; Newtonian random walk; persistent random walk; Random walk; recurrence; scaling limits; time-inhomogeneous Markov-processes; transience", } @Article{Ramirez:2022:CCB, author = "Alejandro F. Ram{\'\i}rez and Rodrigo Ribeiro", title = "Computable criteria for ballisticity of random walks in elliptic random environment", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--38", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP856", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Computable-criteria-for-ballisticity-of-random-walks-in-elliptic-random/10.1214/22-EJP856.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Ballisticity; criteria; Primary 60K37; random environments; Random walks; secondary 82D30", } @Article{Rivera-Lopez:2022:LCO, author = "Kelvin Rivera-Lopez and Douglas Rizzolo", title = "The leftmost column of ordered {Chinese} restaurant process up-down chains: intertwining and convergence", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--22", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP843", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17; 60J35; 60C05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-leftmost-column-of-ordered-Chinese-restaurant-process-up-down/10.1214/22-EJP843.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Functional limit theorem; intertwining; ordered Chinese restaurant process; up-down Markov chains", } @Article{Tanaka:2022:GED, author = "Ryokichi Tanaka and Kenkichi Tsunoda", title = "{Glauber}-exclusion dynamics: rapid mixing regime", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--26", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP865", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82C22; 60J27; 82C20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Glauber-Exclusion-dynamics-rapid-mixing-regime/10.1214/22-EJP865.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Glauber-Exclusion process; Hydrodynamic limit; interacting particle systems; mixing times for Markov chains", } @Article{Blanca:2022:MMC, author = "Antonio Blanca and Pietro Caputo and Zongchen Chen and Daniel Parisi and Daniel {\v{S}}tefankovi{\v{c}} and Eric Vigoda", title = "On mixing of {Markov} chains: coupling, spectral independence, and entropy factorization", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--42", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP867", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J10; 82B20; 68Q87", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-mixing-of-Markov-chains--coupling-spectral-independence-and/10.1214/22-EJP867.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Log-Sobolev; MCMC; mixing time; spectral independence; Swendsen--Wang", } @Article{Couzinie:2022:FEP, author = "Yannick Couzini{\'e} and Fabio Martinelli", title = "On a front evolution problem for the multidimensional {East} model", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--30", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP870", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82C20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-a-front-evolution-problem-for-the-multidimensional-East-model/10.1214/22-EJP870.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Cutoff phenomenon; East model; front evolution; interacting particle systems; Kinetically constrained models; renormalization", } @Article{Li:2022:HCS, author = "Xinyi Li and Daisuke Shiraishi", title = "The {H{\"o}lder} continuity of the scaling limit of three-dimensional loop-erased random walk", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--37", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP869", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82B41; 60G18", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-H%c3%b6lder-continuity-of-the-scaling-limit-of-three-dimensional/10.1214/22-EJP869.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Loop-erased random walk; Scaling limit", } @Article{Rath:2022:PTB, author = "Bal{\'a}zs R{\'a}th and Jan M. Swart and M{\'a}rton Sz{\H{o}}ke", title = "A phase transition between endogeny and nonendogeny", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--43", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP872", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82C27; 60K35; 82C26; 60J80", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/A-phase-transition-between-endogeny-and-nonendogeny/10.1214/22-EJP872.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "endogeny; frozen percolation; recursive distributional equation; recursive tree process", } @Article{Kolb:2022:NEF, author = "Martin Kolb and Matthias Liesenfeld", title = "On non-extinction in a {Fleming--Viot}-type particle model with {Bessel} drift", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--28", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP866", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G17", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-non-extinction-in-a-Fleming-Viot-type-particle-model/10.1214/22-EJP866.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "extinction; Fleming-Viot particle system", } @Article{Hobson:2022:CLC, author = "David Hobson and Dominykas Norgilas", title = "A construction of the left-curtain coupling", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--46", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP868", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G42", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/A-construction-of-the-left-curtain-coupling/10.1214/22-EJP868.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brenier's theorem; Convex order; Martingales; Optimal transport", } @Article{Berger:2022:NDP, author = "Quentin Berger and Niccol{\`o} Torri and Ran Wei", title = "Non-directed polymers in heavy-tail random environment in dimension", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--67", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP873", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82D60; 60K37; 60G70", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Non-directed-polymers-in-heavy-tail-random-environment-in-dimension/10.1214/22-EJP873.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "heavy-tail distributions; Random polymer; Random walk; range; sub-diffusivity; Super-diffusivity; weak-coupling limit", } @Article{Lodewijks:2022:JPV, author = "Bas Lodewijks", title = "On joint properties of vertices with a given degree or label in the random recursive tree", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--45", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP877", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C80; 05C05; 05C12", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-joint-properties-of-vertices-with-a-given-degree-or/10.1214/22-EJP877.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "depth; graph distance; high degrees; Kingman coalescent; label; Random recursive tree", } @Article{Fontbona:2022:QMF, author = "Joaqu{\'\i}n Fontbona and Felipe Mu{\~n}oz-Hern{\'a}ndez", title = "Quantitative mean-field limit for interacting branching diffusions", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--32", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP874", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "92D25; 60J85; 60H30; 35Q92", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Quantitative-mean-field-limit-for-interacting-branching-diffusions/10.1214/22-EJP874.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Branching diffusions; Mean-field limit; Optimal transport; Population dynamics; rate of convergence", } @Article{Peski:2022:TPD, author = "Roger Van Peski", title = "$q$-{TASEP} with position-dependent slowing", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--35", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP876", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 05E05", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/q-TASEP-with-position-dependent-slowing/10.1214/22-EJP876.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "interacting particle systems; Macdonald processes", } @Article{Daw:2022:WMS, author = "Lara Daw and Laurent Loosveldt", title = "Wavelet methods to study the pointwise regularity of the generalized {Rosenblatt} process", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--45", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP878", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G18; 60G22; 26A16; 60G17", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Wavelet-methods-to-study-the-pointwise-regularity-of-the-generalized/10.1214/22-EJP878.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "42C40; modulus of continuity; Random series; Rosenblatt process; slow/ordinary/rapid points; wavelet series; Wiener Chaos", } @Article{Bras:2022:TVD, author = "Pierre Bras and Gilles Pag{\`e}s and Fabien Panloup", title = "Total variation distance between two diffusions in small time with unbounded drift: application to the {Euler--Maruyama} scheme", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--19", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP881", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "65C30; 60H35", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Total-variation-distance-between-two-diffusions-in-small-time-with/10.1214/22-EJP881.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Aronson's bounds; Euler--Maruyama scheme; Richardson-Romberg extrapolation; Stochastic differential equation; Total variation", } @Article{Denisov:2022:PAS, author = "Denis Denisov and G{\"u}nter Hinrichs and Martin Kolb and Vitali Wachtel", title = "Persistence of autoregressive sequences with logarithmic tails", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--43", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP879", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G50; 60G40; 60F17", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Persistence-of-autoregressive-sequences-with-logarithmic-tails/10.1214/22-EJP879.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "conditioned process; Exit time; Harmonic function; Random walk", } @Article{Chleboun:2022:PDA, author = "Paul Chleboun and Simon Gabriel and Stefan Grosskinsky", title = "{Poisson--Dirichlet} asymptotics in condensing particle systems", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--35", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP882", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82C22; 82C26", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Poisson--Dirichlet-asymptotics-in-condensing-particle-systems/10.1214/22-EJP882.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Condensation; equivalence of ensembles; interacting particle systems; Poisson--Dirichlet distribution; Random partitions; split-merge dynamics", } @Article{Yearwood:2022:TS, author = "Stephen Yearwood", title = "The topology of {SLE}", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--14", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP871", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J67", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-topology-of-SLE%ce%ba-is-random-for-%ce%ba4/10.1214/22-EJP871.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "SLE", } @Article{Bodo:2022:SIR, author = "Gergely Bod{\'o} and Markus Riedle", title = "Stochastic integration with respect to canonical $ \alpha $ _stable cylindrical {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--23", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP884", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H05; 60G20; 60G52; 28C20", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Stochastic-integration-with-respect-to-canonical-%ce%b1-stable-cylindrical-L%c3%a9vy/10.1214/22-EJP884.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "cylindrical L{\'e}vy process; decoupled tangent sequence; Stable processes; stochastic integration", } @Article{Borga:2022:PLS, author = "Jacopo Borga", title = "The permuton limit of strong-{Baxter} and semi-{Baxter} permutations is the skew {Brownian} permuton", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--53", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP886", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60C05; 60G50; 05A05; 34K50", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/The-permuton-limit-of-strong-Baxter-and-semi-Baxter-permutations/10.1214/22-EJP886.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "permutations; permutons; scaling limits; skew Brownian motions; Stochastic differential equations; two-dimensional random walks in cones", } @Article{Journel:2022:CKA, author = "Lucas Journel and Pierre Monmarch{\'e}", title = "Convergence of the kinetic annealing for general potentials", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--37", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP891", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 46N30", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Convergence-of-the-kinetic-annealing-for-general-potentials/10.1214/22-EJP891.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "hypocoercivity; Langevin diffusion; metastability; simulated annealing; stochastic optimization", } @Article{Eisenbaum:2022:ITE, author = "Nathalie Eisenbaum and Haya Kaspi", title = "Isomorphism theorems, extended {Markov} processes and random interlacements", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--27", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP887", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60A10; 60G05; 60G07; 60G15; 60G53; 60G57; 60J25; 60J35; 60J40; 60J45; 60J55", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See addendum \cite{Eisenbaum:2023:AIT}.", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Isomorphism-theorems-extended-Markov-processes-and-random-interlacements/10.1214/22-EJP887.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "excessive measure; Gaussian free fields; isomorphism theorem; Kuznetsov process; Local time; Markov process; quasi-process; Random interlacements", } @Article{Etheridge:2022:EWO, author = "Alison M. Etheridge and Mitchel D. Gooding and Ian Letter", title = "On the effects of a wide opening in the domain of the (stochastic) {Allen--Cahn} equation and the motion of hybrid zones", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--53", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP888", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H30; 60J70; 60J85; 92D15", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-the-effects-of-a-wide-opening-in-the-domain/10.1214/22-EJP888.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Branching Brownian motion; genetic drift; hybrid zones; Mean curvature flow; Population genetics; reflecting boundary conditions; spatial {\textLambda}-Fleming-Viot", } @Article{Berger:2022:ODP, author = "Quentin Berger and Chien-Hao Huang and Niccol{\`o} Torri and Ran Wei", title = "One-dimensional polymers in random environments: stretching vs. folding", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--45", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP862", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82D60; 60K37; 60G70", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/One-dimensional-polymers-in-random-environments-stretching-vs-folding/10.1214/22-EJP862.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "heavy-tail distributions; Random polymer; Random walk; range; sub-diffusivity; Super-diffusivity; weak-coupling limit", } @Article{deRaynal:2022:MSD, author = "Paul-{\'E}ric Chaudru de Raynal and St{\'e}phane Menozzi", title = "On multidimensional stable-driven stochastic differential equations with {Besov} drift", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--52", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP864", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10; 35R11; 60H50; 35B65", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/On-multidimensional-stable-driven-stochastic-differential-equations-with-Besov-drift/10.1214/22-EJP864.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Besov spaces; dynamics; SDEs with singular drifts; Stable processes", } @Article{Halconruy:2022:MCM, author = "H{\'e}l{\`e}ne Halconruy", title = "{Malliavin} calculus for marked binomial processes and applications", journal = j-ELECTRON-J-PROBAB, volume = "27", number = "??", pages = "1--39", month = "", year = "2022", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP892", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H07; 60J75; 60G55; 60F05; 91G10", bibdate = "Thu Mar 23 15:20:06 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-27/issue-none/Malliavin-calculus-for-marked-binomial-processes-and-applications/10.1214/22-EJP892.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "chaos expansion; Chen-Stein method; Malliavin calculus; Optimal hedging; Poisson Limit Theorems; trinomial market model", } @Article{Nakajima:2023:FTD, author = "Shuta Nakajima and Makoto Nakashima", title = "Fluctuations of two-dimensional stochastic heat equation and {KPZ} equation in subcritical regime for general initial conditions", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--38", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP885", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K37; 60F05; 60G44; 82D60", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Fluctuations-of-two-dimensional-stochastic-heat-equation-and-KPZ-equation/10.1214/22-EJP885.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Edwards-Wilkinson equation; KPZ equation; local limit theorem for polymers; stochastic calculus; Stochastic heat equation", } @Article{Bertacco:2023:MAG, author = "Federico Bertacco", title = "Multifractal analysis of {Gaussian} multiplicative chaos and applications", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--36", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP893", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G57; 60G60; 28A80; 28A78", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Multifractal-analysis-of-Gaussian-multiplicative-chaos-and-applications/10.1214/22-EJP893.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gaussian multiplicative chaos; Liouville Brownian motion; Multifractal analysis; multifractal formalism", } @Article{Houdre:2023:CLT, author = "Christian Houdr{\'e} and {\"U}mit I{\c{s}}lak", title = "A central limit theorem for the length of the longest common subsequences in random words", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--24", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP894", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05A05; 60C05; 60F05; 60F10", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/A-central-limit-theorem-for-the-length-of-the-longest/10.1214/22-EJP894.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "central limit theorem; edit/Levenshtein distance; Last passage percolation; longest common subsequences; optimal alignments; Random permutations; random words; Stein's method; supersequences; Tracy-Widom distribution; Ulam's problem", } @Article{Lacker:2023:SSL, author = "Daniel Lacker and Jiacheng Zhang", title = "Stationary solutions and local equations for interacting diffusions on regular trees", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--37", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP889", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60G10", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Stationary-solutions-and-local-equations-for-interacting-diffusions-on-regular/10.1214/22-EJP889.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gibbs measures; Interacting diffusions; Kesten-McKay law; local equations; Markov random fields; nonlinear Markov processes; regular trees; Repulsive Particle Systems; sparse graphs", } @Article{Fill:2023:DFQ, author = "James Allen Fill and Wei-Chun Hung", title = "Density functions for {QuickQuant} and {QuickVal}", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--50", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP899", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "68P10; 60E05; 60C05", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Density-functions-for-QuickQuant-and-QuickVal/10.1214/22-EJP899.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "asymptotic bounds; convolutions of distributions; densities; integral equations; large deviations; Lipschitz continuity; moment generating functions; perfect simulation; QuickQuant; QuickSelect; QuickVal; searching; tails of densities; tails of distributions", } @Article{Xu:2023:EPS, author = "Lu Xu and Linjie Zhao", title = "Equilibrium perturbations for stochastic interacting systems", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--30", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP900", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 82C22", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Equilibrium-perturbations-for-stochastic-interacting-systems/10.1214/22-EJP900.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "equilibrium perturbation; Exclusion process; Hydrodynamic limit; oscillator chain", } @Article{Bruned:2023:RVT, author = "Yvain Bruned and Foivos Katsetsiadis", title = "Ramification of {Volterra}-type rough paths", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--25", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP890", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60L20; 60L30; 60L70", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Ramification-of-Volterra-type-rough-paths/10.1214/22-EJP890.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Rough paths; Volterra equations", } @Article{Coste:2023:SMC, author = "Simon Coste", title = "Sparse matrices: convergence of the characteristic polynomial seen from infinity", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--40", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP875", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Sparse-matrices--convergence-of-the-characteristic-polynomial-seen-from/10.1214/22-EJP875.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Eigenvalues; random directed graphs; random matrices; Sparse matrices", } @Article{Andriopoulos:2023:SLL, author = "George Andriopoulos and Eleanor Archer", title = "Scaling limit of linearly edge-reinforced random walks on critical {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--64", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP901", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17; 60K37; 60K50; 60J60", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Scaling-limit-of-linearly-edge-reinforced-random-walks-on-critical/10.1214/23-EJP901.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Diffusion in random environment; Dirichlet distribution; Galton--Watson trees; Random walk in random environment; reinforced random walks; slow movement", } @Article{Huveneers:2023:EPP, author = "Fran{\c{c}}ois Huveneers and Fran{\c{c}}ois Simenhaus", title = "Evolution of a passive particle in a one-dimensional diffusive environment", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--31", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP896", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17; 60G15; 60G50", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Evolution-of-a-passive-particle-in-a-one-dimensional-diffusive/10.1214/22-EJP896.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "limit theorems; random walks in dynamical random environment; scaling limits", } @Article{Corwin:2023:ETW, author = "Ivan Corwin and Alan Hammond and Milind Hegde and Konstantin Matetski", title = "Exceptional times when the {KPZ} fixed point violates {Johansson}'s conjecture on maximizer uniqueness", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--81", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP898", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "82C21; 60J25", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Exceptional-times-when-the-KPZ-fixed-point-violates-Johanssons-conjecture/10.1214/22-EJP898.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Airy sheet; Brownian Gibbs property; Exceptional times; Hausdorff dimension; the KPZ fixed point", } @Article{Takeda:2023:LTP, author = "Shosei Takeda and Kouji Yano", title = "Local time penalizations with various clocks for {L{\'e}vy} processes", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--35", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP903", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F05; 60G44; 60G51", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Local-time-penalizations-with-various-clocks-for-L%c3%a9vy-processes/10.1214/23-EJP903.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Conditioning; limit theorem; one-dimensional L{\'e}vy process; Penalization", } @Article{Herzog:2023:GDG, author = "David P. Herzog and Jonathan C. Mattingly and Hung D. Nguyen", title = "{Gibbsian} dynamics and the generalized {Langevin} equation", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--29", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP904", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Gibbsian-dynamics-and-the-generalized-Langevin-equation/10.1214/23-EJP904.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gibbsian dynamics; Invariant measures; Langevin equation with memory", } @Article{Hutchcroft:2023:TAI, author = "Tom Hutchcroft", title = "Transience and anchored isoperimetric dimension of supercritical percolation clusters", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--15", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP905", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60J99", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Transience-and-anchored-isoperimetric-dimension-of-supercritical-percolation-clusters/10.1214/23-EJP905.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "finite clusters; Isoperimetry; percolation; Random walk", } @Article{Iksanov:2023:LTD, author = "Alexander Iksanov and Alexander Marynych and Anatolii Nikitin", title = "Limit theorems for discounted convergent perpetuities {II}", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--22", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP907", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F15; 60F17; 60G50; 60G55", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Limit-theorems-for-discounted-convergent-perpetuities-II/10.1214/23-EJP907.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "exponential functional of Brownian motion; functional central limit theorem; Law of the iterated logarithm; perpetuity", } @Article{Rapenne:2023:IMC, author = "Valentin Rapenne", title = "Invariant measures of critical branching random walks in high dimension", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--38", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP906", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Invariant-measures-of-critical-branching-random-walks-in-high-dimension/10.1214/23-EJP906.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60; branching random walks; Invariant measures; Point processes", } @Article{Yang:2023:HQU, author = "Kevin Yang", title = "{Hairer--Quastel} universality in non-stationarity via energy solution theory", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--26", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP908", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H17", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Hairer-Quastel-universality-in-non-stationarity-via-energy-solution-theory/10.1214/23-EJP908.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "KPZ; Stochastic pde; Universality", } @Article{Rosen:2023:TTP, author = "Jay Rosen", title = "Tightness for thick points in two dimensions", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--45", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP910", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J65", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Tightness-for-thick-points-in-two-dimensions/10.1214/23-EJP910.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Barrier estimates; Thick points; two dimensional sphere", } @Article{Criens:2023:MPM, author = "David Criens and Peter Pfaffelhuber and Thorsten Schmidt", title = "The martingale problem method revisited", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--46", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP902", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G07; 60F17; 60H15; 60G17", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/The-martingale-problem-method-revisited/10.1214/23-EJP902.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "fixed times of discontinuity; limit theorems; local uniform topology; Martingale problem; path space; Semimartingales; Skorokhod topology; stable convergence; Volterra equations; weak-strong convergence", } @Article{Bass:2023:REM, author = "Richard F. Bass", title = "The rate of escape of the most visited site of {Brownian} motion", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--12", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP916", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J55", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/The-rate-of-escape-of-the-most-visited-site-of/10.1214/23-EJP916.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian motion; favorite point; most visited site; Rate of escape", } @Article{Enger:2023:UFL, author = "Timo Enger and Peter Pfaffelhuber", title = "A unified framework for limit results in chemical reaction networks on multiple time-scales", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--33", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP897", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60F17; 60J35; 60J76; 60K35", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/A-unified-framework-for-limit-results-in-chemical-reaction-networks/10.1214/22-EJP897.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "functional central limit thoerem; Markov jump process; stochastic averaging", } @Article{Champagnat:2023:GCS, author = "Nicolas Champagnat and Denis Villemonais", title = "General criteria for the study of quasi-stationarity", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--84", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/22-EJP880", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "37A25; 60B10; 60F99; 60J05; 60J10; 60J25; 60J27; 60J60; 60J75; 60J80; 93E03", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/General-criteria-for-the-study-of-quasi-stationarity/10.1214/22-EJP880.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "birth and death processes; Diffusion processes; Galton--Watson processes; Markov processes with absorption; mixing property; perturbed dynamical systems; Q-process; quasi-stationary distribution; reducible processes", } @Article{Fill:2023:CSP, author = "James Allen Fill and Svante Janson", title = "Corrigendum to: The sum of powers of subtree sizes for conditioned {Galton--Watson} trees", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--2", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP915", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C05; 60F05; 60C05; 30E99", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Corrigendum-to--The-sum-of-powers-of-subtree-sizes/10.1214/23-EJP915.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "additive functional; Brownian excursion; conditioned Galton--Watson tree; generating function; Hadamard product of sequences; method of moments; polylogarithm; Random analytic function; simply generated random tree; Singularity analysis; subtree sizes; tree recurrence", } @Article{Galeati:2023:SES, author = "Lucio Galeati and Chengcheng Ling", title = "Stability estimates for singular {SDEs} and applications", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--31", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP913", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H10; 60H50; 60F15; 60J60", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Stability-estimates-for-singular-SDEs-and-applications/10.1214/23-EJP913.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "SDEs with singular coefficients; stability; Krylov--R{\"o}ckner condition; distributional drifts; McKean--Vlasov equations; strong compactness of solutions; Wong--Zakai theorem", } @Article{Leo:2023:BSN, author = "Gayral L{\'e}o and Sablik Mathieu", title = "On the {Besicovitch}-stability of noisy random tilings", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--38", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP917", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "37B51; 37A50; 60K35; 82B43", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/On-the-Besicovitch-stability-of-noisy-random-tilings/10.1214/23-EJP917.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Besicovitch distance; percolation; Robinson tiling; stability; Subshift of finite type", } @Article{Le:2023:SSB, author = "Khoa L{\^e}", title = "Stochastic sewing in {Banach} spaces", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--22", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP918", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H99; 46N30; 60H50", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Stochastic-sewing-in-Banach-spaces/10.1214/23-EJP918.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Local time; martingale type; stochastic regularization; stochastic sewing", } @Article{Gotze:2023:LSS, author = "F. G{\"o}tze and A. Tikhomirov", title = "On the largest and the smallest singular value of sparse rectangular random matrices", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--18", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP919", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B20", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/On-the-largest-and-the-smallest-singular-value-of-sparse/10.1214/23-EJP919.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Marchenko--Pastur law; random matrices; Sample covariance matrices", } @Article{Albenque:2023:RCP, author = "Marie Albenque and {\'E}ric Fusy and Thomas Leh{\'e}ricy", title = "Random cubic planar graphs converge to the {Brownian} sphere", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--54", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP912", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C10; 05C12; 05C80; 60C05; 60D05; 82B41", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Random-cubic-planar-graphs-converge-to-the-Brownian-sphere/10.1214/23-EJP912.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Brownian sphere; Planar graphs; planar maps; Random geometry", } @Article{Peskir:2023:SFD, author = "Goran Peskir and David Roodman", title = "Sticky {Feller} diffusions", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--28", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP909", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J60; 60J65; 60H20; 35C15; 35K20; 35K67", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Sticky-Feller-diffusions/10.1214/23-EJP909.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Bessel process; Brownian motion; Cox--Ingersoll--Ross model; diffusion local time; Feller branching diffusion; Gamma function; Green function; Kolmogorov forward/backward equation; Kummer's confluent hypergeometric function; Laplace transform; Mittag-Leffler function; modified Bessel function; Ornstein--Uhlenbeck process; scale function; slowly reflecting (sticky) boundary behaviour; Speed measure; sticky (Feller) boundary condition; Stochastic differential equation; Time change; transition probability density function; Tricomi's confluent hypergeometric function; Vasicek model", } @Article{Ang:2023:SLC, author = "Morris Ang and Nina Holden and Xin Sun", title = "The {SLE} loop via conformal welding of quantum disks", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--20", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP914", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J67; 60G60", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/The-SLE-loop-via-conformal-welding-of-quantum-disks/10.1214/23-EJP914.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Liouville quantum gravity; Schramm-Loewner evolution", } @Article{Nandan:2023:SPS, author = "Shubhamoy Nandan", title = "Spatial populations with seed-banks in random environment: {III}. {Convergence} towards mono-type equilibrium", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--36", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP922", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B12; 60K37; 60K35; 92D10; 92D25", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Spatial-populations-with-seed-banks-in-random-environment--III/10.1214/23-EJP922.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "clustering; Coexistence; Duality; Equilibrium; fixation probability; Interacting particle system; migration; Moran model; random environment; Resampling; seed-bank", } @Article{Henry:2023:TRS, author = "Beno{\^\i}t Henry and Sylvie M{\'e}l{\'e}ard and Viet Chi Tran", title = "Time reversal of spinal processes for linear and non-linear branching processes near stationarity", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--27", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP911", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "92D25; 92D15; 60J80; 60K35; 60F99", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Time-reversal-of-spinal-processes-for-linear-and-non-linear/10.1214/23-EJP911.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "ancestral path; birth-death processes; competition; genealogy; interaction; jump process; Many-to-One formula; non-local mutation operator; phylogeny; stochastic individual-based models", } @Article{Dewan:2023:MFB, author = "Vivek Dewan and Stephen Muirhead", title = "Mean-field bounds for {Poisson--Boolean} percolation", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--24", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP923", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60G60; 60F99", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Mean-field-bounds-for-Poisson-Boolean-percolation/10.1214/23-EJP923.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "continuum percolation; Critical exponents; mean-field bounds; Poisson-Boolean model", } @Article{Coulson:2023:LCS, author = "Matthew Coulson and Guillem Perarnau", title = "Largest component of subcritical random graphs with given degree sequence", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--28", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP921", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C80; 05C82; 60C05; 60F05", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Largest-component-of-subcritical-random-graphs-with-given-degree-sequence/10.1214/23-EJP921.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "component structure; configuration model; largest component; Local limit theorems; random graph with given degree sequence", } @Article{Conchon-Kerjan:2023:AGG, author = "Guillaume Conchon-Kerjan", title = "Anatomy of a {Gaussian} giant: supercritical level-sets of the free field on regular graphs", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--60", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP920", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60G15; 60C05; 05C80", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Anatomy-of-a-Gaussian-giant--supercritical-level-sets-of/10.1214/23-EJP920.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gaussian free field; percolation; Random graphs", } @Article{Chen:2023:GFE, author = "Zhen-Qing Chen and Jie-Ming Wang", title = "Green function estimates for second order elliptic operators in non-divergence form with {Dini} continuous coefficients", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--54", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP925", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "31B25; 35J08; 60J45", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Green-function-estimates-for-second-order-elliptic-operators-in-non/10.1214/23-EJP925.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "boundary Harnack principle; Green function; Harmonic function; interior Schauder's estimate; Martin integral representation", } @Article{Bethuelsen:2023:LLT, author = "Stein Andreas Bethuelsen and Matthias Birkner and Andrej Depperschmidt and Timo Schl{\"u}ter", title = "Local limit theorems for a directed random walk on the backbone of a supercritical oriented percolation cluster", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--54", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP924", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35; 60K37; 60J10; 82B43", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Local-limit-theorems-for-a-directed-random-walk-on-the/10.1214/23-EJP924.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "environment viewed from the particle; Oriented percolation; quenched local limit theorem in random environment; random walk in dynamical random environment; supercritical cluster", } @Article{Tang:2023:NSC, author = "Pengfei Tang", title = "A note on some critical thresholds of {Bernoulli} percolation", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--22", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP926", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60K35", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/A-note-on-some-critical-thresholds-of-Bernoulli-percolation/10.1214/23-EJP926.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "60CO5; Bernoulli percolation; critical probability; cutset; periodic trees", } @Article{Yamazaki:2023:TDM, author = "Kazuo Yamazaki", title = "Three-dimensional magnetohydrodynamics system forced by space-time white noise", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--66", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP929", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "35B65; 35Q85; 35R60", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Three-dimensional-magnetohydrodynamics-system-forced-by-space-time-white-noise/10.1214/23-EJP929.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Gaussian hypercontractivity; magnetohydrodynamics system; Paracontrolled distributions; renormalization; Wick products", } @Article{Aksamit:2023:GBR, author = "Anna Aksamit and Libo Li and Marek Rutkowski", title = "Generalized {BSDE} and reflected {BSDE} with random time horizon", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--41", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP927", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60H30; 60H10; 60G40; 91G40", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Generalized-BSDE-and-reflected-BSDE-with-random-time-horizon/10.1214/23-EJP927.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "BSDE; credit risk; Enlargement of filtration; random time; Reflected BSDE", } @Article{Matsui:2023:SDI, author = "Muneya Matsui", title = "Subexponentialiy of densities of infinitely divisible distributions", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--29", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP928", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60E07; 60G70; 62F12", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Subexponentialiy-of-densities-of-infinitely-divisible-distributions/10.1214/23-EJP928.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "almost decreasing; asymptotic to a non-increasing function; Infinite divisibility; long-tailedness; L{\'e}vy measure; subexponential density; tail equivalence", } @Article{Banerjee:2023:DCR, author = "Sayan Banerjee and Xiangying Huang", title = "Degree centrality and root finding in growing random networks", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--39", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP930", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "05C82; 60J85; 60J28", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Degree-centrality-and-root-finding-in-growing-random-networks/10.1214/23-EJP930.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "attachment functions; continuous time branching processes; degree centrality; network centrality measures; Persistence; root finding algorithms", } @Article{Chitour:2023:GBD, author = "Yacine Chitour and Guilherme Mazanti and Pierre Monmarch{\'e} and Mario Sigalotti", title = "On the gap between deterministic and probabilistic {Lyapunov} exponents for continuous-time linear systems", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--39", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP932", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J25; 34A38; 34D08", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/On-the-gap-between-deterministic-and-probabilistic-Lyapunov-exponents-for/10.1214/23-EJP932.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "continuous-time Markov processes; convexified Markov processes; linear switched systems; Lyapunov exponents; Piecewise deterministic Markov processes", } @Article{Angst:2023:FSZ, author = "J{\"u}rgen Angst and Guillaume Poly", title = "Fluctuations in {Salem--Zygmund} almost sure {Central Limit Theorem}", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--40", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP931", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "26C10; 30C15; 42A05; 60F17; 60G55", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Fluctuations-in-SalemZygmund-almost-sure-Central-Limit-Theorem/10.1214/23-EJP931.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "almost sure CLT; Noise sensitivity; random trigonometric polynomials; Universality", } @Article{Eisenbaum:2023:AIT, author = "Nathalie Eisenbaum and Haya Kaspi", title = "Addendum to {``Isomorphism} theorems, extended {Markov} processes and random interlacements''", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--3", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP935", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60A10; 60G05; 60G07; 60G15; 60G53; 60G57; 60J25; 60J35; 60J40; 60J45; 60J55", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", note = "See \cite{Eisenbaum:2022:ITE}.", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Addendum-to-Isomorphism-theorems-extended-Markov-processes-and-random-interlacements/10.1214/23-EJP935.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "excessive measure; Gaussian free fields; isomorphism theorem; Kuznetsov process; Local time; Markov process; quasi-process; Random interlacements", } @Article{Fakhry:2023:EMP, author = "Rami Fakhry and Dapeng Zhan", title = "Existence of multi-point boundary {Green}'s function for chordal {Schramm--Loewner} evolution {(SLE)}", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--29", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP936", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60J67", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Existence-of-multi-point-boundary-Greens-function-for-chordal-Schramm/10.1214/23-EJP936.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Green's function; Schramm-Loewner evolution; SLE", } @Article{Pfaffelhuber:2023:DPM, author = "Peter Pfaffelhuber and Anton Wakolbinger", title = "A diploid population model for copy number variation of genetic elements", journal = j-ELECTRON-J-PROBAB, volume = "28", number = "??", pages = "1--15", month = "", year = "2023", CODEN = "????", DOI = "https://doi.org/10.1214/23-EJP934", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "92D15; 60J80; 60F17; 60G57", bibdate = "Thu Mar 23 15:20:18 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/A-diploid-population-model-for-copy-number-variation-of-genetic/10.1214/23-EJP934.full", acknowledgement = ack-nhfb, ajournal = "Electron. J. Probab.", fjournal = "Electronic Journal of Probability", journal-URL = "https://projecteuclid.org/euclid.ejp", keywords = "Feller branching diffusion; Poisson approximation; slow-fast system; transposable elements", } %% [23-Mar-2023] TO DO: check for incomplete v28