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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...
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作者：Zhu, Qingsan
作者单位：Nanjing University of Aeronautics & Astronautics
摘要：We study critical branching random walks and introduce the branching capacity and related concepts for any finite subset of Zd,d >= 5 . By introducing these concepts, we can obtain analogues of various classical results for random walks. In this paper, we develop the basic properties of the branching capacity and show that it is closely related to the probability of visiting a fixed finite set by a critical branching random walk starting from a distant point, as well as to the conditional dist...
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作者：Ryou, Donggeun; Suomala, Ville
作者单位：Indiana University System; Indiana University Bloomington; University of Oulu
摘要：We consider multifractal Mandelbrot cascades supported on planar C2 curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the measure.
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作者：Bansaye, Vincent; Berah, Tresnia; Cloez, Bertrand
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Institut Agro; Universite de Montpellier; INRAE
摘要：We consider branching processes for structured populations: each individual is characterised by a type or trait which belongs to a general measurable state space. We focus on the supercritical recurrent case, where the population may survive and grow and the trait distribution converges to a probability measure. The branching process is then expected to be driven by the positive triplet of first eigenvalue problem of the first moment semigroup. Under the assumption of convergence of the renorm...
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作者：Grama, Ion; Quint, Jean-Francois; Xiao, Hui
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Montpellier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper represents the first step toward achieving this goal, specifically entailing the construction of a novel entity - the target harmonic measure. This measure, together with the harmonic function, serves as a pivotal component in establishing the conditioned local limit theorem. Using a reversal identity, we in...
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作者：Deuschel, Jean-Dominique; Kumagai, Takashi; Slowik, Martin
作者单位：Technical University of Berlin; Waseda University; University of Mannheim
摘要：In this paper we consider a time-continuous random walk in Z(d) in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these random conductances are stationary and ergodic and, moreover, that they are bounded from below but unbounded from above with finite first moment. We derive sharp on-diagonal estimates for the annealed first and second discrete space derivative of the heat kernel which then yield local limit theorems for the corresponding kernels...
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作者：Denisov, Denis; Fitzgerald, Will; Wachtel, Vitali
作者单位：University of Manchester; University of Bielefeld
摘要：The Airy line ensemble is a random collection of continuous ordered paths that plays an important role within random matrix theory and the Kardar-Parisi-Zhang universality class. The aim of this paper is to prove a universality property of the Airy line ensemble. We study growing numbers of i.i.d. continuous-time random walks which are then conditioned to stay in the same order for all time using a Doob h-transform. We consider a general class of increment distributions; a sufficient condition...
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作者：Bacallado, Sergio; Sabot, Christophe; Tarres, Pierre
作者单位：Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS)
摘要：We define a linearly reinforced process called the (*)-Edge-Reinforced Random Walk ((*)-ERRW) which can be seen as a Yaglom reversible, hence non-reversible, extension of the Edge-Reinforced Random Walk (ERRW) introduced by Coppersmith and Diaconis in 1986 [4]. This family of processes also generalizes the r-dependent ERRW introduced by Bacallado et al. in 2009 [3]. Under some assumptions on the initial weights, the (*)-ERRW is partially exchangeable in the sense of Diaconis and Freedman [5], ...
