-
作者：Bolthausen, Erwin; Zeitouni, Ofer
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Zurich; Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：We present a multiscale analysis for the exit measures from large balls in Z(d), d >= 3, of random walks in certain i.i.d. random environments which are small perturbations of the fixed environment corresponding to simple random walk. Our main assumption is an isotropy assumption on the law of the environment, introduced by Bricmont and Kupiainen. Under this assumption, we prove that the exit measure of the random walk in a random environment from a large ball, approaches the exit measure of a...
-
作者：Attal, Stephane; Belton, Alexander C. R.
作者单位：University College Cork; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：Suppose Z = (Zt) (t >= 0) is a normal martingale which satisfies the structure equation d[Z](t) = (alpha(t) + beta(t)Z(t-))dZ(t) + dt. By adapting and extending techniques due to Parthasarathy and to Kurtz, it is shown that, if alpha is locally bounded and beta has values in the interval [- 2,0], the process Z is unique in law, possesses the chaotic- representation property and is strongly Markovian ( in an appropriate sense). If also beta is bounded away from the endpoints 0 and 2 on every co...
-
作者：Dembo, Amir; Gantert, Nina; Peres, Yuval; Shi, Zhan
作者单位：Stanford University; University of Munster; University of California System; University of California Berkeley; Sorbonne Universite; Universite Paris Cite
摘要：Let xi (n, x) be the local time at x for a recurrent one-dimensional random walk in random environment after n steps, and consider the maximum xi*(n) = max(x) xi(n, x). It is known that lim sup(n)xi(n)/n is a positive constant a.s. We prove that lim inf(n)(log log log n)xi*(n)/n is a positive constant a.s.;this answers a question of P. Revesz [5]. The proof is based on an analysis of the valleys in the environment, defined as the potential wells of record depth. In particular, we show that alm...
-
作者：Bolley, Francois; Guillin, Arnaud; Villani, Cedric
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Universite PSL; Universite Paris-Dauphine
摘要：We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.
-
作者：Ginovyan, M. S.; Sahakyan, A. A.
作者单位：Boston University; National Academy of Sciences of Armenia; Institute of Mathematics - NAS RA
摘要：Let X(t), t is an element of R, be a centered real-valued stationary Gaussian process with spectral density f (lambda). The paper considers a question concerning asymptotic distribution of Toeplitz type quadratic functional Q(T) of the process X(t), generated by an integrable even function g(lambda). Sufficient conditions in terms of f (lambda) and g(lambda) ensuring central limit theorems for standard normalized quadratic functionals Q(T) are obtained, extending the results of Fox and Taqqu (...
-
作者：Vargas, Vincent
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：In this article, we derive strong localization results for directed polymers in random environment. We show that at low temperature the polymer measure is asymptotically concentrated at a few points of macroscopic mass (we call these points is an element of-atoms). These results are derived assuming weak conditions on the tail decay of the random environment.
-
作者：Johansson, K.
作者单位：Royal Institute of Technology
摘要：The Tracy-Widom distribution that has been much studied in recent years can be thought of as an extreme value distribution. We discuss interpolation between the classical extreme value distribution exp(- exp(-x)), the Gumbel distribution, and the Tracy-Widom distribution. There is a family of determinantal processes whose edge behaviour interpolates between a Poisson process with density exp(-x) and the Airy kernel point process. This process can be obtained as a scaling limit of a grand canon...
-
作者：Chistyakov, G. P.; Goetze, F.
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
摘要：We extend the classical Darmois-Skitovich theorem to the case where the linear forms L-r1 = U1X1 +center dot center dot center dot+ UnXn and L-r2 = Un+1X1+center dot center dot center dot+U2nXn have random coefficients U-1,...,U-2n. Under minimal restrictions on the random coefficients we completely describe the distributions of the independent random variables X-1,...,X-n and U-1,...,U-2n such that the linear forms L-r1 and L-r2 are independent.
-
作者：Gozlan, Nathael; Leonard, Christian
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre
摘要：New transportation cost inequalities are derived by means of elementary large deviation reasonings. Their dual characterization is proved; this provides an extension of a well-known result of S. Bobkov and F. Gotze. Their tensorization properties are investigated. Sufficient conditions (and necessary conditions too) for these inequalities are stated in terms of the integrability of the reference measure. Applying these results leads to new deviation results: concentration of measure and deviat...
-
作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.
