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作者：Johnson, Tobias; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：Consider the sum of d many i.i.d. random permutation matrices on n labels along with their transposes. The resulting matrix is the adjacency matrix of a random regular (multi)-graph of degree 2d on n vertices. It is known that the distribution of smooth linear eigenvalue statistics of this matrix is given asymptotically by sums of Poisson random variables. This is in contrast with Gaussian fluctuation of similar quantities in the case of Wigner matrices. It is also known that for Wigner matric...
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作者：Moreno Flores, Gregorio R.
作者单位：Pontificia Universidad Catolica de Chile
摘要：We give a new proof of the fact that the solutions of the stochastic heat equation, started with nonnegative initial conditions, are strictly positive at positive times. The proof uses concentration of measure arguments for discrete directed polymers in Gaussian environments, originated in M. Talagrand's work on spin glasses and brought to directed polymers by Ph. Carmona and Y. Hu. We also get slightly improved bounds on the lower tail of the solutions of the stochastic heat equation started ...
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作者：Garet, Olivier; Marchand, Regine
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The asymptotic shape theorem for the contact process in random environment gives the existence of a norm mu on R-d such that the hitting time t(x) is asymptotically equivalent to mu(x) when the contact process survives. We provide here exponential upper bounds for the probability of the event {t(x)/mu(x) is not an element of[1 - epsilon, 1 + epsilon]); these bounds are optimal for independent random environment. As a special case, this gives the large deviation inequality for the contact proce...
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作者：Caputo, Pietro; Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan; Toninelli, Fabio Lucio
作者单位：Roma Tre University; Microsoft; University of California System; University of California Berkeley; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We study the Glauber dynamics for the (2 + 1)D Solid-On-Solid model above a hard wall and below a far away ceiling, on an L x L box of Z(2) with zero boundary conditions, at large inverse-temperature P. It was shown by Bricmont, El Mellouki and Frohlich [J. Stat. Phys. 42 (1986) 743-798] that the floor constraint induces an entropic repulsion effect which lifts the surface to an average height H um log L. As an essential step in understanding the effect of entropic repulsion on the Glauber dyn...
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作者：Cerrai, Sandra; Da Prato, Giuseppe
作者单位：University System of Maryland; University of Maryland College Park; Scuola Normale Superiore di Pisa
摘要：We consider the Kolmogorov operator associated with a reaction diffusion equation having polynomially growing reaction coefficient and perturbed by a noise of multiplicative type, in the Banach space E of continuous functions. By analyzing the smoothing properties of the associated transition semigroup, we prove a modification of the classical identite du carre des champs that applies to the present non-Hilbertian setting. As an application of this identity, we construct the Sobolev space W-1,...
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作者：Meerschaert, Mark M.; Straka, Peter
作者单位：Michigan State University; University of New South Wales Sydney
摘要：Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their finite-dimensional distributions is an important open problem. This paper develops a general semi-Markov theory for CTRW limit processes in R-d with infinitely many particle jumps (renewals) in finite time intervals. The particle jumps and waiting times can ...
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作者：Procaccia, Eviatar B.; Shellef, Eric
作者单位：University of California System; University of California Los Angeles; Weizmann Institute of Science
摘要：Let a simple random walk run inside a torus of dimension three or higher for a number of steps which is a constant proportion of the volume. We examine geometric properties of the range, the random subgraph induced by the set of vertices visited by the walk. Distance and mixing bounds for the typical range are proven that are a k-iterated log factor from those on the full torus for arbitrary k. The proof uses hierarchical renormalization and techniques that can possibly be applied to other ran...
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作者：Sidorova, Nadia; Twarowski, Aleksander
作者单位：University of London; University College London
摘要：The parabolic Anderson model is the Cauchy problem for the heat equation on the integer lattice with a random potential xi. We consider the case when {xi(z) : z is an element of Z(d)} is a collection of independent identically distributed random variables with Weibull distribution with parameter 0 < gamma < 2, and we assume that the solution is initially localised in the origin. We prove that, as time goes to infinity, the solution completely localises at just one point with high probability, ...
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作者：Ding, Jian; Zeitouni, Ofer
作者单位：Stanford University; University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between the two largest maxima, and an estimate for the right tail up to a multiplicative constant on the law of the centered maximum.
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作者：Kabluchko, Zakhar; Zaporozhets, Dmitry
作者单位：Ulm University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：Let xi(0), xi(1,) . . . be independent identically distributed complex-valued random variables such that E log(1 + vertical bar xi(0)vertical bar) < infinity. We consider random analytic functions of the form G(n)(z) = Sigma xi(k)f(k,n)Z(k), where f(k,n) are deterministic complex coefficients. Let mu(n) be the random measure counting the complex zeros of G(n) according to their multiplicities. Assuming essentially that -1/nlog f([tn]),(n) -> u(t) as n -> infinity, where u(t) is some function, ...
