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作者：Damron, Michael; Hanson, Jack; Harper, David; Lam, Wai-Kit
作者单位：University System of Georgia; Georgia Institute of Technology; City University of New York (CUNY) System; City College of New York (CUNY); National Taiwan University; University of Minnesota System; University of Minnesota Twin Cities
摘要：In first-passage percolation (FPP), we let(tau(v))be i.i.d. nonnegative weights on thevertices of a graph and study the weight of the minimal path between distant vertices. If Fi s the distribution function of tau v, there are different regimes: if F(0) is small,this weight typically grows like a linear function of the distance, and when F(0) islarge, the weight is typically of order one. In between these is the critical regime inwhich the weight can diverge, but does so sublinearly. We study ...
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作者：Kolliopoulos, Nikolaos; Larsson, Martin; Zhang, Zeyu
作者单位：Carnegie Mellon University
摘要：We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as those arising in an i.i.d. system where each particle follows the associated McKean-Vlasov limiting dynamics. Because the maximum depends on all particles, our result does not follow from classical propagation of chaos, where convergence to an i.i.d. limit ...
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作者：Angel, Omer; Ray, Gourab; Spinka, Yinon
作者单位：University of British Columbia; University of Victoria; Tel Aviv University
摘要：From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the hyperbolic plane and regular trees. The result for the Euclidean space relies on a novel 0-1 law for stationary processes. Towards establishing the results for the hyperbolic plane and regular trees, we prove an upper bound on the density of any well-separated set ...
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作者：Huesmann, Martin; Mattesini, Francesco; Otto, Felix
作者单位：University of Munster; Max Planck Society
摘要：We show that there is no cyclically monotone stationary matching of two independent Poisson processes in dimension d = 2. The proof combines the harmonic approximation result from Goldman et al. (Commun. Pure Appl. Math. 74:2483-2560, 2021) with local asymptotics for the two-dimensional matching problem for which we give a new self-contained proof using martingale arguments.
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作者：Dinh, Tien-Cuong; Kaufmann, Lucas; Wu, Hao
作者单位：National University of Singapore; Institute for Basic Science - Korea (IBS); Centre National de la Recherche Scientifique (CNRS); Universite de Orleans
摘要：We obtain various new limit theorems for random walks on SL2(C) under low moment conditions. For non-elementary measures with a finite second moment we prove a Local Limit Theorem for the norm cocycle, yielding the optimal version of a theorem of E. Le Page. For measures with a finite third moment, we obtain the Local Limit Theorem for the matrix coefficients, improving a recent result of Grama-Quint-Xiao and the authors, and Berry-Esseen bounds with optimal rate O(1/root n) for the norm cocyc...
