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作者：Gorin, Vadim; Kenyon, Richard
作者单位：University of California System; University of California Berkeley; Yale University
摘要：We study limit shapes in two equivalent models: the six-vertex model in the c -> 0 limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-Lagrange equation for the limit shape and show how to solve it for a class of rectilinear polygonal domains. Its solutions are given by piecewise-algebraic functions with lines of discontinuities.
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作者：Mukherjee, Chiranjib; Recke, Konstantin
作者单位：University of Munster
摘要：Let G be the Cayley graph of a finitely generated, infinite group Gamma . We show that Gamma has the Haagerup property if and only if for every alpha<1 , there is a Gamma -invariant bond percolation P on G with E[deg(omega)(g)]>alpha degG(g) for every vertex g and with the two-point function tau(g,h)=P[g <-> h] vanishing as d(g,h)->infinity . As an upshot, we also obtain a sufficient condition for the Haagerup property using Bernoulli percolation and the associated threshold pconn of random co...
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作者：Hartung, Lisa; Louidor, Oren; Wu, Tianqi
作者单位：Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：In this work, we resolve three open questions which were raised recently concerning the limiting extremal and cluster point processes of branching Brownian Motion. The former process records the heights of all extreme values of the motion, while the latter records the relative heights of extreme values in a genealogical neighborhood of order unity around a local maximum thereof. For the extremal point process, we show that first order asymptotics for its mass away from zero holds almost-surely...
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作者：Jorritsma, Joost; Komjathy, Julia; Mitsche, Dieter
作者单位：University of Oxford; Delft University of Technology; Pontificia Universidad Catolica de Chile
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作者：Ganguly, Ankan; Spiliopoulos, Konstantinos; Sussman, Daniel
作者单位：Boston University
摘要：We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include n agents, whose opinions are given by latent stochastic processes, and a dynamic network process describing agent interactions. Models in this class incorporate (a) bi-directional feedback between the latent processes and the network process, (b) persistence effects, meaning that the network structure at the current time depe...
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作者：Can, Van Hao; Kubota, Naoki; Nakajima, Shuta
作者单位：Vietnam Academy of Science & Technology (VAST); Nihon University; Keio University
摘要：In this paper, we study the upper tail large deviation for the one-dimensional frog model. In this model, sleeping and active frogs are assigned to sites of Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}$$\end{document}. While sleeping frogs do not move, the active ones move as independent simple rand...
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作者：Qin, Shuo
摘要：Under suitable moment assumptions, we show that a genuinely d-dimensional step-reinforced random walk undergoes a phase transition between recurrence and transience in dimensions d=1,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=1,2$$\end{document}, and that it is transient for all reinforcement parameters in ...
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作者：Bates, Erik; Emrah, Elnur; Martin, James; Seppalainen, Timo; Sorensen, Evan
作者单位：North Carolina State University; University College Dublin; University of Oxford; University of Wisconsin System; University of Wisconsin Madison; Columbia University
摘要：In i.i.d. exponential last-passage percolation, we describe the joint distribution of Busemann functions, over all edges and over all directions, in terms of a joint last-passage problem in a finite inhomogeneous environment. More specifically, the Busemann increments within a k & times;& ell; grid, and associated to d different directions, are equal in distribution to a particular collection of last-passage increments inside a (k+d-1)& times;(& ell;+d-1) grid. The joint Busemann distribution ...
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作者：Schmid, Dominik; Yang, Zongrui
作者单位：University of Augsburg; Columbia University
摘要：We consider the stationary measure of the open asymmetric simple exclusion process (ASEP) with light particles. We prove several results on the asymptotic locations of the light particles under the stationary measure. Moreover, in the fan region of the high and low density phases, we study the mixing times for open ASEP with light particles. Our approach involves the matrix product ansatz, Askey-Wilson signed measures, moderate deviation results for second class particles, as well as various c...
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作者：Dewitt, Jonathan; Dolgopyat, Dmitry
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University System of Maryland; University of Maryland College Park
摘要：In this paper, we prove several theorems relating annealed exponential mixing of the two-point motion with quenched properties of the one-point motion for conservative IID random dynamical systems. In particular, we show that annealed exponential mixing of the two-point motion implies quenched exponential mixing of the one-point motion. We also show that if the two-point motion satisfies annealed exponential mixing and the annealed central limit theorem with polynomial rate of convergence, the...
