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作者：Auffinger, Antonio; Damron, Michael
作者单位：University of Chicago; Princeton University
摘要：In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663-697] proved a long standing conjecture that relates the transversal exponent and the fluctuation exponent x in first-passage percolation on Z(d). The purpose of this paper is to replace the main argument of Chatterjee (2013) and give an alternative proof of this relation. Specifically, we show that under the assumption that exponents defined in Chatterjee (2013) exist, one has the relation x <= 2 xi - 1. One advantage ...
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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：Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin
作者单位：Hebrew University of Jerusalem; Microsoft; Stanford University
摘要：We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree distributions and, more generally, the limiting distribution of subgraphs in balls of any given radius k around a random vertex in the preferential attachment graph. We also establish the finite-volume corrections which give the approach to the limit.
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作者：Kyprianou, Andreas E.; Carlos Pardo, Juan; Watson, Alexander R.
作者单位：University of Bath; CIMAT - Centro de Investigacion en Matematicas
摘要：We consider two first passage problems for stable processes, not necessarily symmetric, in one dimension. We make use of a novel method of path. censoring in order to deduce explicit formulas for hitting probabilities, hitting distributions and a killed potential measure. To do this, we describe in full detail the Wiener-Hopf factorization of a new Lamperti-stable-type Levy process obtained via the Lamperti transform, in the style of recent work in this area.
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作者：Li, Zenghu
作者单位：Beijing Normal University
摘要：A family of continuous-state branching processes with immigration are constructed as the solution flow of a stochastic equation system driven by time space noises. The family can be regarded as an inhomogeneous increasing path-valued branching process with immigration. Two nonlocal branching immigration superprocesses can be defined from the flow. We identify explicitly the branching and immigration mechanisms of those processes. The results provide new perspectives into the tree-valued Markov...
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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, ...
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作者：Gess, Benjamin
作者单位：Humboldt University of Berlin
摘要：Unique existence of solutions to porous media equations driven by continuous linear multiplicative space time rough signals is proven for initial data in L-1(O) on bounded domains O. The generation of a continuous, order-preserving random dynamical system on L-1(O) and the existence of a random attractor for stochastic porous media equations perturbed by linear multiplicative noise in space and time is obtained. The random attractor is shown to be compact and attracting in L-infinity(O) norm. ...
