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作者：Cattiaux, P.; Gentil, I.; Guillin, A.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincare inequalities, general Beckner inequalities, etc.). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincare inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
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作者：van der Hofstad, Remco; den Hollander, Frank; Slade, Gordon
作者单位：Leiden University; Leiden University - Excl LUMC; Eindhoven University of Technology; University of British Columbia
摘要：We consider critical spread-out oriented percolation above 4 + 1 dimensions. Our main result is that the extinction probability at time n (i.e., the probability for the origin to be connected to the hyperplane at time n but not to the hyperplane at time n + 1) decays like 1/Bn-2 as n -> infinity, where B is a finite positive constant. This in turn implies that the survival probability at time n (i.e., the probability that the origin is connected to the hyperplane at time n) decays like 1/Bn-2 ...
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作者：Pinelis, Iosif
作者单位：Michigan Technological University
摘要：Let BS1,..., BSn be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter p is an element of (0,1). Let m(*)(p) := (1 + p + 2p(2))/(2 root p - p(2) + 4p(2)) if 0 < p <= 1/2 and m(*)(p) := 1 if 1/2 <= p < 1. Let m >= m(*)(p). Let f be such a function that f and f '' are nondecreasing and convex. Then it is proved that for all nonnegative numbers c(1),..., c(n) one has the inequality Ef(c(1)BS(1) + center dot center dot center dot...
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作者：Bass, Richard F.; Lavrentiev, Alexander
作者单位：University of Connecticut; University of Wisconsin System
摘要：We consider the degenerate elliptic operator acting on C-b(2) functions on [0,infinity) (d): [GRAPHIC] where the a(i) are continuous functions that are bounded above and below by positive constants, the bi are bounded and measurable, and the alpha(i) is an element of (0, 1). We impose Neumann boundary conditions on the boundary of [0,infinity)(d). There will not be uniqueness for the submartingale problem corresponding to L. If we consider, however, only those solutions to the submartingale pr...
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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...
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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...
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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...
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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.
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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 (...
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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.
