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作者：Bordenave, Charles; Caputo, Pietro; Salez, Justin
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Roma Tre University; Universite Paris Cite
摘要：A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the context of card shuffling (Aldous and Diaconis in Am Math Mon 93:333-348, 1986), this remarkable phenomenon is now rigorously established for many reversible chains. Here we consider the non-reversible case of random walks on sparse directed graphs, for whi...
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作者：Sapozhnikov, Artem; Shiraishi, Daisuke
作者单位：Leipzig University; Kyoto University
摘要：We provide a decomposition of the trace of the Brownian motion into a simple path and an independent Brownian soup of loops that intersect the simple path. More precisely, we prove that any subsequential scaling limit of the loop erased random walk is a simple path (a new result in three dimensions), which can be taken as the simple path of the decomposition. In three dimensions, we also prove that the Hausdorff dimension of any such subsequential scaling limit lies. We conjecture that our dec...
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作者：Muirhead, Stephen; Pymar, Richard; Sidorova, Nadia
作者单位：University of Oxford; University of London; University College London; University of London; University College London; University of London; Birkbeck University London
摘要：The parabolic Anderson model on with i.i.d. potential is known to completely localise if the distribution of the potential is sufficiently heavy-tailed at infinity. In this paper we investigate a modification of the model in which the potential is partially duplicated in a symmetric way across a plane through the origin. In the case of potential distribution with polynomial tail decay, we exhibit a surprising phase transition in the model as the decay exponent varies. For large values of the e...
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作者：Ding, Jian; Zhang, Fuxi
作者单位：University of Chicago; Peking University
摘要：We consider first passage percolation (FPP) where the vertex weight is given by the exponential of two-dimensional log-correlated Gaussian fields. Our work is motivated by understanding the discrete analog for the random metric associated with Liouville quantum gravity (LQG), which roughly corresponds to the exponential of a two-dimensional Gaussian free field (GFF). The particular focus of the present paper is an aspect of universality for such FPP among the family of log-correlated Gaussian ...
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作者：Basrak, Bojan; Planinic, Hrvoje; Soulier, Philippe
作者单位：University of Zagreb; Universite Paris Saclay
摘要：We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of point process convergence theorem. It is designed to preserve the entire information about the temporal ordering of observations which is typically lost in the limit after time scaling. By going beyond the existing asymptotic theory, we are able to prove a new...
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作者：Gorin, Vadim; Zhang, Lingfu
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; Princeton University
摘要：We study the asymptotics of the global fluctuations for the difference between two adjacent levels in the extension of the classical Jacobi ensemble of random matrices). The limit is identified with the derivative of the 2d Gaussian free field. Our main tools are integral forms for the (Macdonald-type) difference operators originating from the shuffle algebra.
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作者：Monmarche, Pierre
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Universite Gustave-Eiffel
摘要：Combining classical arguments for the analysis of the simulated annealing algorithm with the more recent hypocoercive method of distorted entropy, we prove the convergence for large time of the kinetic Langevin annealing with logarithmic cooling schedule.
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作者：Avena, L.; Jara, M.; Vollering, F.
作者单位：Leiden University; Leiden University - Excl LUMC; Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of Bath
摘要：We consider a random walk (RW) driven by a simple symmetric exclusion process (SSE). Rescaling the RW and the SSE in such a way that a joint hydrodynamic limit theorem holds we prove a joint path large deviation principle. The corresponding large deviation rate function can be split into two components, the rate function of the SSE and the one of the RW given the path of the SSE. These components have different structures (Gaussian and Poissonian, respectively) and to overcome this difficulty ...
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作者：Basu, Riddhipratim; Sidoravicius, Vladas; Sly, Allan
作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; New York University; NYU Shanghai; Princeton University
摘要：We consider the problem of embedding one i.i.d. collection of Bernoulli random variables indexed by it was shown in Basu and Sly(Probab Theory Relat Fields 159:721-775, 2014) to be possible almost surely for sufficiently large M. In this paper we provide a multi-scale argument extending this result to higher dimensions.
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作者：Chafai, Djalil; Tikhomirov, Konstantin
作者单位：Universite PSL; Universite Paris-Dauphine; University of Alberta
摘要：Consider a sample of a centered random vector with unit covariance matrix. We show that under certain regularity assumptions, and up to a natural scaling, the smallest and the largest eigenvalues of the empirical covariance matrix converge, when the dimension and the sample size both tend to infinity, to the left and right edges of the Marchenko-Pastur distribution. The assumptions are related to tails of norms of orthogonal projections. They cover isotropic log-concave random vectors as well ...
