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作者：Rassoul-Agha, Firas; Seppalaineni, Timo
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a 2 + epsilon moment for the step of the walk uniformly in the environment. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
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作者：Birkner, Matthias; Zaehle, Iljana
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
摘要：We show that the centred occupation time process of the origin of a system of critical binary branching random walks in dimension d >= 3, started off either from a Poisson field or in equilibrium, when suitably normalized, converges to a Brownian motion in d >= 4. In d = 3, the limit process is a fractional Brownian motion with Hurst parameter 3/4 when starting in equilibrium, and a related Gaussian process when starting from a Poisson field. For (dependent) branching random walks with state d...
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作者：Benjamini, Itai; Gurel-Gurevich, Ori; Lyons, Russell
作者单位：Weizmann Institute of Science; Indiana University System; Indiana University Bloomington
摘要：We show that the edges crossed by a random walk in a network form a recurrent graph a.s. In fact, the same is true when those edges are weighted by the number of crossings.
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We consider the asymptotic fluctuation behavior of the largest eigenvalue of certain sample covariance matrices in the asymptotic regime where both dimensions of the corresponding data matrix go to infinity. More precisely, let X be an n x p matrix, and let its rows be i.i.d. complex normal vectors with mean 0 and covariance Sigma p. We show that for a large class of covariance matrices Sigma P, the largest eigenvalue of X*X is asymptotically distributed (after recentering and rescaling) as th...
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作者：Hanen, Albert
作者单位：Universite Paris Nanterre
摘要：We study the covariance (for Gibbs measure) of spins at two sites in the case of a Sherrington-Kirkpatrick model with an external field. When the number of sites of the model grows to infinity, an asymptotic evaluation of the p moments of that covariance allows us to obtain a weak limit theorem, with a generally non-Gaussian limit law.
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作者：Merkl, Franz; Rolles, Silke W. W.
作者单位：University of Munich; Technical University of Munich
摘要：In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given by random weights on the edges. The edge weights decay exponentially in space. The process converges to a stationary process. We provide asymptotic bounds for the range of the random walker up to a given time, showing that it localizes much more than an ordi...
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作者：Hairer, M.; Ohashi, A.
作者单位：University of Warwick; Universidade Estadual de Campinas
摘要：We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a class of non-Markovian systems. They allow us to obtain a criteria for ergodicity which is similar in nature to the Doob-Khas'minskii theorem. The second part of this article shows how it is possible to apply these results to the case of stochastic different...
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作者：Balazs, M.; Rassoul-Agha, F.; Seppaelaeinen, T.; Sethuraman, S.
作者单位：Budapest University of Technology & Economics; University of Wisconsin System; University of Wisconsin Madison; Utah System of Higher Education; University of Utah; Iowa State University
摘要：We give a construction of the zero range and bricklayers' processes in the totally asymmetric, attractive case. The novelty is that we allow jump rates to grow exponentially. Earlier constructions have permitted at most linearly growing rates. We also show the invariance and extremality of a natural family of i.i.d. product measures indexed by particle density. Extremality is proved with an approach that is simpler than existing ergodicity proofs.
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作者：Yang, Ming
作者单位：Columbia University
摘要：Let X-t be any additive process in R-d. There are finite indices delta(i), beta(i), i = 1. 2 and a function u, all of which are defined in terms of the characteristics of X-t, such that lim(t -> 0) inf u(t)X--1/n(t)* = {0, if n > delta(1), {infinity, if n < delta(2), lim(t -> 0) sup u(t)X--1/n(t)* = {0, if n > beta(2), a.s., {infinity, if n < beta(1), where X-t(*) = sup(0 < s < t) |X-s|. When X-t is a Levy process with X-0 = 0, delta 1 = delta 2, beta 1 = beta 2 and u(t) = t. This is a special...
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作者：Berestycki, Julien; Berestycki, Nathanaeel; Schweinsberg, Jason
作者单位：Aix-Marseille Universite; University of California System; University of California San Diego; University of British Columbia
摘要：Coalescents with multiple collisions, also known as Lambda-coalescents, were introduced by Pitman and Sagitov in 1999. These processes describe the evolution of particles that undergo stochastic coagulation in such a way that several blocks can merge at the same time to form a single block. In the case that the measure A is the Beta(2-alpha, alpha) distribution, they are also known to describe the genealogies of large populations where a single individual can produce a large number of offsprin...
