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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...
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作者：Seppäläinen, T
作者单位：Iowa State University
摘要：We study the evolution of a small perturbation of the equilibrium of a totally asymmetric one-dimensional interacting system. The model we take as an example is Hammersley's process as seen from a tagged particle, which can be viewed as a process of interacting positive-valued stick heights on the sites of Z. It is known that under Euler scaling (space and time scale n) the empirical stick profile obeys the Burgers equation. We refine this result in two ways. If the process starts close enough...
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作者：Atar, R; Budhiraja, A; Dupuis, P
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Brown University
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作者：Kosygina, E
作者单位：Northwestern University
摘要：The paper studies the behavior of the specific entropy for one-dimensional simple exclusion processes under the hydrodynamic scaling of time and space. It is shown that if the initial configurations possess a macroscopic profile then for each positive macroscopic time the specific microscopic entropy converges to the macroscopic entropy. The latter is defined in terms of the solution of the corresponding hydrodynamic equation.
