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作者：Bass, RF; Rosen, J
作者单位：University of Connecticut; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：For a symmetric random walk in Z(2) with 2 + delta moments, we represent vertical bar R(n)vertical bar, the cardinality of the range, in terms of an expansion involving the renormalized intersection local times of a Brownian motion. We show that for each k >= 1 [Graphics] where Wt is a Brownian motion, W(t)((n)) = Wnt/root n, gamma j,n is the renormalized intersection local time at time 1 for W((n)) and c(X) is a constant depending on the distribution of the random walk.
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作者：Benaïm, M; Raimond, O
作者单位：University of Neuchatel; Universite Paris Saclay
摘要：Let M be a compact Riemannian manifold. A self-interacting diffusion on M is a stochastic process solution to where {W-t} is a Brownian vector field on M and V-x(y) = V(x, y) a smooth function. Let mu(t) = 1/t integral(t)(0) delta X-s ds denote the normalized occupation measure of X-t. We prove that, when V is symmetric, mu(t) converges almost surely to the critical set of a certain nonlinear free energy functional J. Furthermore, J has generically finitely many critical points and mu(t) conve...
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作者：Haydn, N; Lacroix, Y; Vaienti, S
作者单位：University of Southern California; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite
摘要：Given an ergodic dynamical system (X, T, mu), and U subset of X measurable with mu(U) > 0, let mu(U)tau(U)(x) denote the normalized hitting time of x is an element of X to U. We prove that given a sequence (U-n) with mu(U-n) -> 0, the distribution function of the normalized hitting times to U-n converges weakly to some subprobability distribution F if and only if the distribution function of the normalized return time converges weakly to some distribution function and that in the converging ca...
