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作者：Dembo, A; Gantert, N; Peres, Y; Zeitouni, O
作者单位：Stanford University; Stanford University; Helmholtz Association; Karlsruhe Institute of Technology; Hebrew University of Jerusalem; University of California System; University of California Berkeley; Technion Israel Institute of Technology
摘要：In the study of large deviations for random walks in random environment, a key distinction has emerged between quenched asymptotics, conditional on the environment, and annealed asymptotics, obtained from averaging over environments. In this paper we consider a simple random walk {X-n} on a Galton-Watson tree T, i.e., on the family tree arising from a supercritical branching process. Denote by \X-n\ the distance between the node X-n and the root of T. Our main result is the almost sure equalit...
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作者：Lambert, A
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：Recent works by J.F. Le Gall and Y. Le Jan [ 15] have extended the genealogical structure of Galton-Watson processes to continous-state branching processes (CB). We are here interested in processes with immigration (CBI). The height process H which contains all the information about this genealogical structure is defined as a simple local time functional of a strong Markov process X*, called the genealogy-coding process (GCP). We first show its existence using Ito's synthesis theorem. We then ...
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作者：Bendikov, A; Saloff-Coste, L
作者单位：Cornell University
摘要：Consider a central Gaussian convolution semigroup (mu(t))(t>0) on a connected compact semisimple group. Then either the measure mu(t) is singular with respect to Haar measure for all t > 0, or there exists a time t such that mu(t) is absolutely continuous with respect to Haar measure and admits a continuous density.
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作者：Carmona, P; Hu, Y
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：The purpose of this work is the study of the partition function Z(n) (beta) of a (d + 1)-dimensional lattice directed polymer in a Gaussian random environment (beta > 0 being the inverse of temperature). In the low-dimensional cases (d = 1 or d = 2), we prove that for all beta > 0, the renormalized partition function Z(n) (beta)/EZ(n) (beta) converges to 0 and the,))() of two independent configurations does not converge to 0. In the correlation ((n)) high dimensional case (d > 3), a lower tail...
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作者：Mazza, C; Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：The well known convergence of the spectrum of large random symmetric matrices, due to Wigner, holds for products of correlated symmetric matrices with general entries. The limiting moments coincide with weighted enumeration of permutations, or of rooted trees. When the correlations are Markovian, the limiting first moments are closely related to Carlitz-Riordan q-Catalan numbers. As a consequence, these moments asymptotically exhibit a phase transition, with respect to the correlation coeffici...
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作者：Li, WBV; Shao, QM
作者单位：University of Delaware; University of Oregon
摘要：Let xi = (xi(i), 1 less than or equal to i less than or equal to n) and eta = (eta(t), 1 less than or equal to i less than or equal to n) be standard normal random variables with covariance matrices R-1 = (r(j,i)(1)) and R-0 = (r(j,i)(0)), resplectively, Slepian's lemma says that if r(j,i)(1) greater than or equal to r(j,i)(0) for 1 less than or equal to i, j less than or equal to n, the lower bound P (xi(t) < u for 1 <1 < n)/P(eta(i) less than or equal to u for 1 less than or equal to i less ...
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作者：Finnoff, W
摘要：We investigate large-deviation properties for systems of probability kernels and these kernels when integrated with respect to a system of measures that also satisfy the large-deviation principle. The results of our analysis are then used to demonstrate the large-deviation property and derive rate functions for systems of measures derived from the distributions of evolutionary game processes.
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作者：Coutin, L; Qian, ZM
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：In this paper we show, by using dyadic approximations, the existence of geometric rough path associated with a fractional Brownian motion with Hurst parameter greater than 1/4. Using the integral representation of fractional Brownian motions, we futhermore obtain a Skohorod integral representation of the geometric rough path we constructed. By the results in [Ly1], a stochastic integration theory may be established for fractional Brownian motions, and strong solutions and Wong-Zakai type limit...
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作者：Collet, P; Martinez, S; Schmitt, B
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universidad de Chile; Universidad de Chile; Universite Bourgogne Europe
摘要：We prove an exponential inequality for the absolutely continuous invariant measure of a piecewise expanding map of the interval. As an immediate corollary we obtain a concentration inequality. We apply these results to the estimation of the rate of convergence of the empirical measure in various metrics and also to the efficiency of the shadowing by sets of positive measure.
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作者：Külske, C
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Can the joint measures of quenched disordered lattice spin models (with finite range) on the product of spin-space and disorder-space be represented as (suitably generalized) Gibbs measures of an annealed system? - We prove that there is always a potential (depending on both spin and disorder variables) that converges absolutely on a set of full measure w.r.t. the joint measure (weak Gibbsianness). This positive result is surprising when contrasted with the results of a previous paper [K6], wh...
