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作者：Bovier, Anton; Gayrard, Veronique
作者单位：University of Bonn; Aix-Marseille Universite
摘要：We derive a general criterion for the convergence of clock processes in random dynamics in random environments that is applicable in cases when correlations are not negligible, extending recent results by Gayrard [(2010), (2011), forthcoming], based on general criterion for convergence of sums of dependent random variables due to Durrett and Resnick [Ann. Probab. 6 (1978) 829-846]. We demonstrate the power of this criterion by applying it to the case of random hopping time dynamics of the p-sp...
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作者：Gill, Hardeep
作者单位：University of British Columbia
摘要：We construct a supercritical interacting measure-valued diffusion with representative particles that are attracted to, or repelled from, the center of mass. Using the historical stochastic calculus of Perkins, we modify a super Ornstein-Uhlenbeck process with attraction to its origin, and prove continuum analogues of results of Englander [Electron. J. Probab. 15 (2010) 1938-1970] for binary branching Brownian motion. It is shown, on the survival set, that in the attractive case the mass normal...
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作者：Ivanov, Alexander V.; Leonenko, Nikolai; Ruiz-Medina, Maria D.; Savich, Irina N.
作者单位：Ministry of Education & Science of Ukraine; Igor Sikorsky Kyiv Polytechnic Institute; Cardiff University; University of Granada
摘要：The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear functionals of Gaussian stationary processes with singular spectra.
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作者：Pene, Francoise; Saussol, Benoit; Zweimueller, Roland
作者单位：Universite de Bretagne Occidentale; University of Vienna
摘要：We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as epsilon -> 0, of the return time to (-epsilon, epsilon). We then refine this result by establishing a limit theorem for the hitting-time distributions of (x - epsilon, x + epsilon) with arbitrary x is an element of R.
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作者：Sabot, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z(d), RWDE are parameterized by a 2d-tuple of positive reals called weights. In this paper, we characterize for d >= 3 the weights for which there exists an absolutely continuous invariant probability distribution for the process viewed from the particle. We can deduce from this result ...
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作者：Kuelbs, James; Kurtz, Thomas; Zinn, Joel
作者单位：University of Wisconsin System; University of Wisconsin Madison; Texas A&M University System; Texas A&M University College Station
摘要：For stochastic processes {X-t : t is an element of E}, we establish sufficient conditions for the empirical process based on {I-Xt <= y - Pr(X-t <= y) : t is an element of E, y is an element of R} to satisfy the CLT uniformly in t is an element of E, y is an element of R. Corollaries of our main result include examples of classical processes where the CLT holds, and we also show that it fails for Brownian motion tied down at zero and E = [0, 1].
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作者：Addario-Berry, Louigi; Devroye, Luc; Janson, Svante
作者单位：McGill University; McGill University; Uppsala University
摘要：We study the height and width of a Galton-Watson tree with offspring distribution xi satisfying E xi = 1, 0 < Var xi < infinity, conditioned on having exactly n nodes. Under this conditioning, we derive sub-Gaussian tail bounds for both the width (largest number of nodes in any level) and height (greatest level containing a node); the bounds are optimal up to constant factors in the exponent. Under the same conditioning, we also derive essentially optimal upper tail bounds for the number of no...
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作者：Bramson, Maury; Burdzy, Krzysztof; Kendall, Wilfrid
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Washington; University of Washington Seattle; University of Warwick
摘要：Two random processes X and Y on a metric space are said to be epsilon-shy coupled if there is positive probability of them staying at least a positive distance E apart from each other forever. Interest in the literature centres on nonexistence results subject to topological and geometric conditions; motivation arises from the desire to gain a better understanding of probabilistic coupling. Previous nonexistence results for co-adapted shy coupling of reflected Brownian motion required convexity...
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作者：Miller, Jason
作者单位：Stanford University
摘要：Let X-1, X-2 be independent random walks on Z(n)(d), d >= 3, each starting from the uniform distribution. Initially, each site of Z(n)(d) is unmarked, and, whenever X-i visits such a site, it is set irreversibly to i. The mean of vertical bar A(i)vertical bar, the cardinality of the set A(i) of sites painted by i, once all of Z(n)(d) has been visited, is 1/2n(d) by symmetry. We prove the following conjecture due to Pemantle and Peres: for each d >= 3 there exists a constant alpha(d) such that ...
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作者：Oliveira, Roberto Imbuzeiro
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We prove an upper bound for the epsilon-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to T-RW(G) ln(vertical bar V vertical bar/epsilon), where vertical bar V vertical bar is the number of vertices in G, and T-RW(G) is the 1/4-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clusters, the giant component of the Erdos-...
