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作者：Birkner, Matthias; Sun, Rongfeng
作者单位：Johannes Gutenberg University of Mainz; National University of Singapore
摘要：We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as c root t logt. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.
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作者：Goncalves, Patricia; Landim, Claudio; Milanes, Aniura
作者单位：Universidade de Lisboa; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal de Minas Gerais
摘要：We consider one-dimensional, boundary driven, weakly asymmetric exclusion processes in contact with reservoirs at fixed density. For a general set of initial measures and by using a microscopic Cole-Hopf transformation, we derive the nonequilibrium fluctuations which are given by a generalized Ornstein-Uhlenbeck process.
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作者：Antunovic, Tonci; Procaccia, Eviatar B.
作者单位：University of California System; University of California Los Angeles; Texas A&M University System; Texas A&M University College Station
摘要：We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and by relying on ergodic theorems, we prove that almost surely all trees are finite. Using the mass transport principle, we generalize the result to Eden model in graphs of the form G x z(+), where G is a Cayley graph. This generalizes certain known results on the two-type Richardson model, in partic...
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作者：Frieze, Alan; Pegden, Wesley
作者单位：Carnegie Mellon University
摘要：Given an instance of the preferential attachment graph G(n) = ([n], E-n), we would like to find vertex 1, using only local information about the graph; that is, by exploring the neighborhoods of small sets of vertices. Borgs et al. gave an algorithm which runs in time O(log(4) n), which is local in the sense that at each step, it needs only to search the neighborhood of a set of vertices of size O(log(4) n). We give an algorithm to find vertex 1, which w.h.p. runs in time O (omega log n) and w...
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作者：van den Berg, Jacob; Nolin, Pierre
作者单位：Centrum Wiskunde & Informatica (CWI); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study a percolation model on the square lattice, where clusters freeze (stop growing) as soon as their volume (i.e., the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when they reach diameter at least N was studied in van den Berg, de Lima and Nolin [Random Structures Algorithms 40 (2012) 220-226] and Kiss [Probab. Theory Related Fields 163 (2015) 713-768]. Using volume as a way to measure the size of a cluster instead of diamete...
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作者：Ley, Christophe; Reinert, Gesine; Swan, Yvik
作者单位：Ghent University; University of Oxford; University of Liege
摘要：this paper, we propose tight upper and lower bounds for the Wasser-stein distance between any two univariate continuous distributions with probability densities p(1) and p(2) having nested supports. These explicit bounds are expressed in terms of the derivative of the likelihood ratio p(1)/p(2) as well as the Stein kernel tau(1) of p(1). The method of proof relies on a new variant of Stein's method which manipulates Stein operators. We give several applications of these bounds. Our main applic...
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作者：Arguin, Louis-Pierre; Belius, David; Harper, Adam J.
作者单位：Universite de Montreal; City University of New York (CUNY) System; Baruch College (CUNY); City University of New York (CUNY) System; New York University
摘要：A recent conjecture of Fyodorov-Hiary-Keating states that the maximum of the absolute value of the Riemann zeta function on a typical bounded interval of the critical line is exp{loglogT - 3/4logloglogT + O(1)}, for an interval at (large) height T. In this paper, we verify the first two terms in the exponential for a model of the zeta function, which is essentially a randomized Euler product. The critical element of the proof is the identification of an approximate tree structure, present also...
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作者：Ball, Frank; Brittont, Tom; Trapman, Pieter
作者单位：University of Nottingham; Stockholm University
摘要：Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size n. A Markovian SIR (susceptible -> infective -> recovered) infectious disease, having importation of infectives, taking place in this population is analysed. The main situation treated is where n -> infinity, keeping the basic reproduction number R-0 as well as the importation rate of infectives fixed, but assuming that the quotient of the avera...
