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作者：Romik, Dan
作者单位：University of California System; University of California Davis
摘要：The arctic circle theorem of Jockusch, Propp, and Shor asserts that uniformly random domino tilings of an Aztec diamond of high order are frozen with asymptotically high probability outside the arctic circle inscribed within the diamond. A similar arctic circle phenomenon has been observed in the limiting behavior of random square Young tableaux. In this paper, we show that random domino tilings of the Aztec diamond are asymptotically related to random square Young tableaux in a more refined s...
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作者：Kern, Peter; Meerschaert, Mark M.; Scheffler, Hans-Peter
作者单位：Heinrich Heine University Dusseldorf; Michigan State University; Universitat Siegen
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作者：Dawson, Donald A.; Li, Zenghu
作者单位：Carleton University; Beijing Normal University
摘要：We first prove some general results on pathwise uniqueness, comparison property and existence of nonnegative strong solutions of stochastic equations driven by white noises and Poisson random measures. The results are then used to prove the strong existence of two classes of stochastic flows associated with coalescents with multiple collisions, that is, generalized Fleming-Viot flows and flows of continuous-state branching processes with immigration. One of them unifies the different treatment...
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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：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...
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作者：Tarres, Pierre; Toth, Balint; Valko, Benedek
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Budapest University of Technology & Economics; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the asymptotic behavior of a self-interacting one-dimensional Brownian polymer first introduced by Durrett and Rogers [Probab. Theory Related Fields 92 (1992) 337-349] The polymer describes a stochastic process with a drift which is a certain average of its local time. We show that a smeared out version of the local time function as viewed from the actual position of the process is a Markov process in a suitably chosen function space, and that this process has a Gaussian stationary me...
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作者：Drewitz, Alexander; Ramirez, Alejandro F.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Pontificia Universidad Catolica de Chile
摘要：Consider a random walk in an uniformly elliptic environment in dimensions larger than one. In 2002, Sznitman introduced for each gamma is an element of (0, 1) the ballisticity condition (T)(gamma) and the condition (T') defined as the fulfillment of (T)gamma for each gamma is an element of (0, 1). Sznitman proved that (T') implies a ballistic law of large numbers. Furthermore, he showed that for all gamma is an element of (0.5, 1), (T)gamma is equivalent to (T'). Recently, Berger has proved th...
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作者：McGoff, Kevin
作者单位：University System of Maryland; University of Maryland College Park
摘要：Let X be an irreducible shift of finite type (SFT) of positive entropy, and let B-n(X) be its set of words of length n. Define a random subset omega of B-n(X) by independently choosing each word from B-n(X) with some probability alpha. Let X-omega be the (random) SET built from the set omega. For each 0 <= alpha <= 1 and n tending to infinity, we compute the limit of the likelihood that X-omega is empty, as well as the limiting distribution of entropy for X-omega. For alpha near 1 and n tendin...
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作者：Fukushima, Masatoshi; Uemura, Toshihiro
作者单位：University of Osaka; Kansai University
摘要：Let E be a locally compact separable metric space and in be a positive Radon measure on it. Given a nonnegative function k defined on E x E off the diagonal whose anti-symmetric part is assumed to be less singular than the symmetric part, we construct an associated regular lower bounded semi-Dirichlet form eta on L-2(E; m) producing a Hunt process X-0 on E whose jump behaviours are governed by k. For an arbitrary open subset D C E, we also construct a Hunt process X-D,X-0 on D in an analogous ...
