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作者：Borodin, Alexei; Bufetov, Alexey
作者单位：Massachusetts Institute of Technology (MIT); University of Bonn; University of Bonn
摘要：We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or multi-species) ASEP and stochastic vertex models for a certain class of initial/boundary conditions, generalizing previous results of Amir-AngelValko and Borodin-Wheeler. We are also able to use the symmetry, together with previously known results for uncolored model...
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作者：Gwynne, Ewain; Pfeffer, Joshua
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Let M be the infinite spanning-tree-weighted random planar map, which is the local limit of finite random planar maps sampled with probability proportional to the number of spanning trees they admit. We show that a.s. the M-graph-distance diameter of the external diffusion-limited aggregation (DLA) cluster on M run for m steps is of order m(2/d+om(1)), where d is the metric ball volume growth exponent for M (which was shown to exist by Ding and Gwynne (Comm. Math. Phys. 374 (2020) 1877-1934). ...
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作者：Dauvergne, Duncan; Virag, Balint
作者单位：Princeton University; University of Toronto
摘要：The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper is to provide a set of tools, which allow for precise probabilistic analysis of the Airy line ensemble. The two main theorems are a representation in terms of independent Brownian bridges connecting a fine grid of points, and a modulus of continuity result for all lines. Along the way, we give tail bounds and moduli of continuity for noninte...
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作者：Berggren, Tomas
作者单位：University of Michigan System; University of Michigan
摘要：In this paper we consider domino tilings of the Aztec diamond with doubly periodic weightings. In particular, a family of models which, for any k is an element of N, includes models with k smooth regions is analyzed as the size of the Aztec diamond tends to infinity. We use a nonintersecting paths formulation and give a double integral formula for the correlation kernel of the Aztec diamond of finite size. By a classical steepest descent analysis of the correlation kernel, we obtain the local ...
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作者：Crane, Edward; Rath, Balazs; Yeo, Dominic
作者单位：University of Bristol; MTA-BME Stochastics Research Group; Budapest University of Technology & Economics; University of Oxford
摘要：We study the distribution of ages in the mean field forest fire model introduced by Rath and Toth. This model is an evolving random graph whose dynamics combine Erdos-Renyi edge-addition with a Poisson rain of lightning strikes. All edges in a connected component are deleted when any of its vertices is struck by lightning. We consider the asymptotic regime of lightning rates for which the model displays self-organized criticality. The age of a vertex increases at unit rate, but it is reset to ...
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作者：Bhattacharya, Bhaswar B.; Bhattacharya, Sohom; Ganguly, Shirshendu
作者单位：University of Pennsylvania; Stanford University; University of California System; University of California Berkeley
摘要：In this paper, we consider the problem of estimating the joint upper and lower tail large deviations of the edge eigenvalues of an Erdos-Renyi random graph G(n,p), in the regime of p where the edge of the spectrum is no longer governed by global observables, such as the number of edges, but rather by localized statistics, such as high degree vertices. Going beyond the recent developments in mean-field approximations of related problems, this paper provides a comprehensive treatment of the larg...
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作者：Sarkar, Sourav; Virag, Balint
作者单位：University of Toronto; University of Toronto
摘要：We show that the law of the KPZ fixed point starting from arbitrary initial condition is absolutely continuous with respect to the law of Brownian motion B on every compact interval. In particular, the Airy(1) process is absolutely continuous with respect to B on any compact interval.
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作者：Coste, Simon; Salez, Justin
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We confirm the long-standing prediction that c = e approximate to 2.718 is the thresh-old for the emergence of a nonvanishing absolutely continuous part (extended states) at zero in the limiting spectrum of the Erdos-Renyi random graph with average degree c. This is achieved by a detailed second-order analysis of the resolvent (A - z)(-1) near the singular point z = 0, where A is the adjacency operator of the Poisson-Galton-Watson tree with mean offspring c. More generally, our method applies ...
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作者：Dubach, Guillaume; Peled, Yuval
作者单位：Institute of Science & Technology - Austria; New York University
摘要：We consider words G(i1) . . . G(im) involving i.i.d. complex Ginibre matrices and study tracial expressions of their eigenvalues and singular values. We show that the limit distribution of the squared singular values of every word of length m is a Fuss-Catalan distribution with parameter m + 1. This generalizes previous results concerning powers of a complex Ginibre matrix and products of independent Ginibre matrices. In addition, we find other combinatorial parameters of the word that determi...
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作者：Aggarwal, Amol; Lopatto, Patrick; Marcinek, Jake
作者单位：Columbia University; Institute for Advanced Study - USA; Harvard University
摘要：We analyze statistics for eigenvector entries of heavy-tailed random symmetric matrices (also called Levy matrices) whose associated eigenvalues are sufficiently small. We show that the limiting law of any such entry is nonGaussian, given by the product of a normal distribution with another random variable that depends on the location of the corresponding eigenvalue. Although the latter random variable is typically nonexplicit, for the median eigenvector it is given by the inverse of a one-sid...
