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作者：Blumenthal, Alex; Zelati, Michele Coti; Gvalani, Rishabh S.
作者单位：University System of Georgia; Georgia Institute of Technology; Imperial College London; Max Planck Society
摘要：We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that allows us to construct space-time smooth, uniformly bounded in time, universal exponential mixers. The framework is then applied to the problem of proving exponential mixing in a classical example proposed by Pierrehumbert in 1994, consisting of alternating periodic shear flows with randomized phases. This settles a ...
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作者：Bertini, Lorenzo; Gabrielli, Davide; Landim, Claudio
作者单位：Sapienza University Rome; University of L'Aquila
摘要：We consider the weakly asymmetric exclusion process on the d-dimensional torus. We prove a large deviations principle for the time averaged empirical density and current in the joint limit in which both the time interval and the number of particles diverge. This result is obtained both by analyzing the variational convergence, as the number of particles diverges, of the Donsker-Varadhan functional for the empirical process and by considering the large time behavior of the hydrodynamical rate f...
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作者：Alimohammadi, Yeganeh; Borgs, Christian; Saberi, Amin
作者单位：Stanford University; University of California System; University of California Berkeley
摘要：We study random digraphs on sequences of expanders with a bounded average degree which converge locally in probability. We prove that the rel-ative size and the threshold for the existence of a giant strongly connected component as well as the asymptotic fraction of nodes with giant fan-in or nodes with giant fan-out are local, in the sense that they are the same for two sequences with the same local limit. The digraph has a bow-tie structure, with all but a vanishing fraction of nodes lying e...
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作者：Alishahi, Kasra; Barzegar, Milad; Zamani, Mohammadsadegh
作者单位：Sharif University of Technology; University of Yazd
摘要：We prove that every negatively associated sequence of Bernoulli random variables with summable covariances has a trivial tail a-field. A corollary of this result is the tail triviality of strongly Rayleigh processes. This is a gen-eralization of a result due to Lyons, which establishes tail triviality for dis-crete determinantal processes. We also study the tail behavior of negatively associated Gaussian and Gaussian threshold processes. We show that these processes are tail trivial though, in...
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作者：Schmid, Dominik
作者单位：University of Bonn
摘要：We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a segment of size N with open boundaries. We focus on the maximal current phase and prove that the mixing time is of order N3/2, up to logarithmic corrections. In the triple point, where the TASEP with open boundaries approaches the Uniform distribution on the state space, we show that the mixing time is precisely of order N3/2. This is conjectured to be the correct order of the mixing time for a wide range of...
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作者：Xiao, Hui; Grama, Ion; Liu, Quansheng
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider (gn)n>1 a sequence of independent and identically distributed random matrices and the left random walk Gn := gn . . . g1, n > 1 on the general linear group GL(d, R). Under suitable conditions we establish a Bahadur-Rao-Petrov type large deviation expansion for the coefficient (f, Gnv) of the product Gn, where v & epsilon; Rd and f & epsilon; (Rd)*. In particular, we obtain an explicit rate function in the large deviation principle, thus im-proving significantly the known large deviati...
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作者：Angel, Omer; Holmes, Mark; Ramirez, Alejandro
作者单位：University of British Columbia; University of Melbourne; New York University; NYU Shanghai; Pontificia Universidad Catolica de Chile
摘要：We give nontrivial upper and lower bounds on the range of the so-called Balanced Excited Random Walk in two dimensions and verify a conjecture of Benjamini, Kozma and Schapira. To the best of our knowledge, these are the first nontrivial results for this two-dimensional model.
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作者：Najnudel, Joseph; Paquette, Elliot; Simm, Nick
作者单位：University of Bristol; McGill University; University of Sussex
摘要：We study the secular coefficients of N x N random unitary matrices UN drawn from the Circular-Ensemble which are defined as the coefficients of {zn} in the characteristic polynomial det(1 - zU*N). When > 4, we obtain a new class of limiting distributions that arise when both n and N tend to infinity simultaneously. We solve an open problem of Diaconis and Gamburd (Electron. J. Combin. 11 (2004/06) 2) by showing that, for = 2, the mid-dle coefficient of degree n = N2 j tends to zero as N -oo. W...
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作者：Chong, Carsten; Kevei, Peter
作者单位：Columbia University; Szeged University
摘要：We show that the spatial profile of the solution to the stochastic heat equation features multiple layers of intermittency islands if the driving noise is non-Gaussian. On the one hand, as expected, if the noise is sufficiently heavy-tailed, the largest peaks of the solution will be taller under multiplica-tive than under additive noise. On the other hand, surprisingly, as soon as the noise has a finite moment of order d2, where dis the spatial dimension, the largest peaks will be of the same ...
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作者：Sjostrand, Jonas
作者单位：Malardalen University
摘要：A locally uniform random permutation is generated by sampling n points independently from some absolutely continuous distribution p on the plane and interpreting them as a permutation by the rule that i maps to j if the ith point from the left is the jth point from below. As n tends to infinity, decreas-ing subsequences in the permutation will appear as curves in the plane, and by interpreting these as level curves, a union of decreasing subsequences give rise to a surface. We show that, under...
