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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：Suppose that d >= 2 and alpha is an element of (1, 2). Let D be a bounded C-1,C-1 open set in R-d and b an R-d-valued function on R-d whose components are in a certain Kato class of the rotationally symmetric a-stable process. In this paper, we derive sharp two-sided heat kernel estimates for L-b = Delta(alpha/2) + b . del in D with zero exterior condition. We also obtain the boundary Harnack principle for L-b in D with explicit decay rate.
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider continuous time random interlacements on Z(d), d >= 3, and characterize the distribution of the corresponding stationary random field of occupation times. When d = 3, we relate this random field to the two-dimensional Gaussian free field pinned at the origin by looking at scaled differences of occupation times of long rods by random interlacements at appropriately tuned levels. In the main asymptotic regime, a scaling factor appears in the limit, which is independent of the free fi...
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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：Bianchi, Alessandra; Bovier, Anton; Ioffe, Dmitry
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bonn; Technion Israel Institute of Technology
摘要：We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a meta-stable set. In the example of the Random Field Curie Weiss model, we show that these ideas can also be used to prove asymptotic exponentiallity of normalized metastable escape times.
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作者：Albeverio, Sergio; Kusuoka, Seiichiro
作者单位：University of Bonn; Kyoto University
摘要：The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular domains are shrinking to graphs. The methods we use are probabilistic ones. For shrinking, we use big potentials, respectively, reflection on the boundary of tubes. We show that there exists a unique limit process, and we characterize the limit process by a second...
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作者：Ding, Jian; Lubetzky, Eyal; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：Let C-1 be the largest component of the Erdos-Renyi random graph G(n, p). The mixing time of random walk on C-1 in the strictly supercritical regime, p = c/n with fixed c > 1, was shown to have order log(2) n by Fountoulakis and Reed, and independently by Benjamini, Kozma and Wormald. In the critical window, p = (1 + epsilon)/n where lambda = epsilon(3)n is bounded, Nachmias and Peres proved that the mixing time on C-1 is of order n. However, it was unclear how to interpolate between these res...
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作者：Letac, Gerard; Piccioni, Mauro
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Sapienza University Rome
摘要：In a recent paper [Statist. Probab. Lett. 78 (2008) 1711-1721] it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function F-2(1). In the present paper we fully exploit a formula due to Thomae [J. Reine Angew. Math. 87 (1879) 26-73] in order to generalize substantially the class of random continuous fractions with a density of the above form. This involves the design of seven particular graphs. Infinite paths on th...
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作者：Liu, Jingchen
作者单位：Columbia University
摘要：This paper develops asymptotic approximations of P(f(T) e(f(t)) dt > b) as b -> infinity for a homogeneous smooth Gaussian random field, f, living on a compact d-dimensional Jordan measurable set T. The integral of an exponent of a Gaussian random field is an important random variable for many generic models in spatial point processes, portfolio risk analysis, asset pricing and so forth. The analysis technique consists of two steps: 1. evaluate the tail probability P(f(Xi) e(f(t)) dt > b) over...
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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 ...
