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作者：Giacomin, G; Olla, S; Spohn, H
作者单位：Universite Paris Cite; CY Cergy Paris Universite; Institut Polytechnique de Paris; Ecole Polytechnique; Technical University of Munich; University of Munich; Technical University of Munich
摘要：We study the large scale space-time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space-time scale these fluctuations are governed by an infinite-dimensional Ornstein-Uhlenbeek process. Its effective diffusion type covariance matrix is characterized through a variational formula.
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作者：Burdzy, K; Chen, ZQ
作者单位：University of Washington; University of Washington Seattle
摘要：We define a local time flow of skew Brownian motions, that is, a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a version of the Ray-Knight theorem on local times. In our case, however, the local time process viewed as a function of the spatial variable is a pure jump Markov process ...
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作者：Sznithman, AS
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We introduce in this article a class of transient random walks in a random environment on Z(d). When d greater than or equal to 2, these walks are ballistic and we derive a law of large numbers, a central limit theorem and large-deviation estimates. In the so-called nestling situation, large deviations in the neighborhood of the segment [0, v], v being the limiting velocity, are critical. They are of special interest in view of their close connection with the presence of traps in the medium, t...
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作者：Stef, A; Tenenbaum, G
作者单位：Universite de Lorraine
摘要：Let F, G be arbitrary distribution functions on the real line and let F, G denote their respective bilateral Laplace transforms. Let K > 0 and let h: R+ --> R+ be continuous, non-decreasing, and such that h(u) greater than or equal to Au-4 for some A > 0 and all u > 0. Under the assumptions that sup \(F) over cap (u)- (G) over cap (u)\ less than or equal to epsilon , (F) over cap (u)+ (G) over cap (u) less than or equal to h(u) (-L less than or equal to u less than or equal to L), 0 less than ...
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作者：Penrose, MD
作者单位：Durham University
摘要：Suppose X = (X-x)(xis an element ofZ)(d) is a white noise process, and H(B), defined for finite subsets B of Z(d), is determined in a stationary way by the restriction of X to B. Using a martingale approach, we prove a central limit theorem (CLT) for H as B becomes large, subject to H satisfying a stabilization condition (the effect of changing X-x at a single site needs to be local). This CLT is then applied to component counts for percolation and Boolean models, to the size of the big cluste...
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作者：Alòs, E; Mazet, O; Nualart, D
作者单位：Autonomous University of Barcelona; University of Barcelona
摘要：In this paper we develop a stochastic calculus with respect to a Gaussian process of the form B-t = integral (t)(0) K(t, s) dW(s), where W is a Wiener process and K(t, s) is a square integrable kernel, using the techniques of the stochastic calculus of variations. We deduce change-of-variable formulas for the indefinite integrals and we study the approximation by Riemann sums. The particular case of the fractional Brownian motion is discussed.
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作者：Bramson, M; Cox, JT; Le Gall, JF
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Syracuse University; Universite PSL; Ecole Normale Superieure (ENS)
摘要：The voter model is one of the standard interacting particle systems. Two related problems for this process are to analyze its behavior, after large times t, for the sets of sites (1) sharing the same opinion as the site 0, and (2) having the opinion that was originally at 0. Results on the sizes of these sets were given by Sawyer (1979) and Bramson and Griffeath (1980). Here, we investigate the spatial structure of these sets in d greater than or equal to 2, which we show converge to quantitie...
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作者：Häggström, O
作者单位：Chalmers University of Technology
摘要：We prove uniqueness of the infinite entangled component for bond percolation on the three-dimensional cubic lattice above the entanglement critical probability. This improves earlier results by Grimmett and Holroyd.
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作者：Volkov, S
作者单位：University of Bristol
摘要：Vertex-reinforced random walk (VRRW), defined by Pemantle, is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on arbitrary graphs and show that on almost all of them, VRRW visits only finitely many vertices with a positive probability. We conjecture that on all graphs of bounded degree, this happens with probability 1, and provide a proof only for trees of this type. We distinguish between several different pa...
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作者：Biskup, M; König, W
作者单位：Microsoft; Technical University of Berlin
摘要：We consider the parabolic Anderson problem partial derivative (t)u = kappa Deltau + xiu on (0, infinity) x Z(d) with random i.i.d. potential xi = (xi (z))(z is an element ofZ)(d) and the initial condition u(0, (.)) equivalent to 1. Our main assumption is that esssup xi (0) = 0. Depending on the thickness of the distribution Prob( xi (0) is an element of (.)) close to its essential supremum, we identify both the asymptotics of the moments of u(t, 0) and the almost-sure asymptotics of u(t, 0) as...
