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作者：Kemp, Todd; Nourdin, Ivan; Peccati, Giovanni; Speicher, Roland
作者单位：University of California System; University of California San Diego; Universite de Lorraine; University of Luxembourg; Saarland University
摘要：We prove that a normalized sequence of multiple Wigner integrals (in a fixed order of free Wigner chaos) converges in law to the standard semicircular distribution if and only if the corresponding sequence of fourth moments converges to 2, the fourth moment of the semicircular law. This extends to the free probabilistic, setting some recent results by Nualart and Peccati on characterizations of central limit theorems in a fixed order of Gaussian Wiener chaos. Our proof is combinatorial, analyz...
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作者：Chen, Zhen-Qing; Kim, Panki; Song, Renming
作者单位：University of Washington; University of Washington Seattle; Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators m - (m(2/alpha) - Delta)(alpha/2)] in C-1,C-1 open sets. Here m > 0 and alpha is an element of (0, 2). The estimates are uniform in m is an element of (0, M] for each fixed M > 0. Letting m down arrow 0, we recover the Dirichlet heat kernel estimates for Delta(alpha/2) := -(-Delta)(alpha/2) in C-1,C-1 open sets obtained in [14]. Sharp ...
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作者：Pittel, Boris
作者单位：University System of Ohio; Ohio State University
摘要：For an ergodic Markov chain {X (t)} on N, with a stationary distribution pi, let T-n > 0 denote a hitting time for [n](c), and let X-n = X (T-n). Around 2005 Guy Louchard popularized a conjecture that, for n -> infinity, T-n is almost Geometric(p), p = pi([n](c)), X-n is almost stationarily distributed on [n](c) and that X-n and T-n are almost independent, if p(n) := sup(i) p(i,[n](c)) -> 0 exponentially fast. For the chains with p(n) -> 0, however slowly, and with sup(i,j) parallel to p(i, .)...
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作者：Keller, Nathan; Mossel, Elchanan; Sen, Arnab
作者单位：Weizmann Institute of Science; University of California System; University of California Berkeley; University of Cambridge
摘要：We present a new definition of influences in product spaces of continuous distributions. Our definition is geometric, and for monotone sets it is identical with the measure of the boundary with respect to uniform enlargement. We prove analogs of the Kahn-Kalai-Linial (KKL) and Talagrand's influence sum bounds for the new definition. We further prove an analog of a result of Friedgut showing that sets with small influence sum are essentially determined by a small number of coordinates. In parti...
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作者：Van den Berg, Jacob; Kiss, Demeter
作者单位：Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam
摘要：Let E be the set of edges of the d-dimensional cubic lattice Z(d), with d >= 2, and let (e), e is an element of E, be nonnegative values. The passage time from a vertex nu to a vertex omega is defined as inf(pi : nu ->omega) Sigma(e is an element of pi) t(e), where the infimum is over all paths pi from nu to omega, and the sum is over all edges e of pi. Benjamini, Kalai and Schramm [2] proved that if the t (e)'s are i.i.d. two-valued positive random variables, the variance of the passage time ...
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作者：van Neerven, Jan; Veraar, Mark; Weis, Lutz
作者单位：Delft University of Technology; Helmholtz Association; Karlsruhe Institute of Technology
摘要：In this article we prove a maximal L-p-regularity result for stochastic convolutions, which extends Krylov's basic mixed L-p(L-q)-inequality for the Laplace operator on R-d to large classes of elliptic operators, both on R-d and on bounded domains in R-d with various boundary conditions. Our method of proof is based on McIntosh's H-infinity-functional calculus, R-boundedness techniques and sharp L-p (L-q)-square function estimates for stochastic integrals in L-q-spaces. Under an additional inv...
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作者：Bendikov, Alexander; Saloff-Coste, Laurent
作者单位：University of Wroclaw; Cornell University
摘要：We study the decay of convolution powers of probability measures without second moment but satisfying some weaker finite moment condition. For any locally compact unimodular group G and any positive function rho : G --> [0, +infinity], we introduce a function Phi(G,rho) which describes the fastest possible decay of n bar right arrow phi((2n)) (e) when phi is a symmetric continuous probability density such that integral rho phi is finite. We estimate Phi(G,rho) for a variety of groups G and fun...
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作者：Kuwae, Kazuhiro
作者单位：Kumamoto University
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作者：Kuwada, Kazumasa
作者单位：Ochanomizu University
摘要：We study an approximation by time-discretized geodesic random walks of a diffusion process associated with a family of time-dependent metrics on manifolds. The condition we assume on the metrics is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow, and no further a priori curvature bound is required. As an application, we construct a coupling by reflection which yields a nice estimate of coupling time, and hence a...
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作者：Patie, P.
作者单位：Universite Libre de Bruxelles
摘要：Let X be a spectrally negative self-similar Markov process with 0 as an absorbing state. In this paper, we show that the distribution of the absorption time is absolutely continuous with an infinitely continuously differentiable density. We provide a power series and a contour integral representation of this density. Then, by means of probabilistic arguments, we deduce some interesting analytical properties satisfied by these functions, which include, for instance, several types of hypergeomet...
