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作者：Gouere, Jean-Baptiste
作者单位：Universite de Orleans
摘要：We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if E(R-d) is finite, where R denotes the radius of the balls around Poisson points and d denotes the dimension. We also give related results concerning the integrability of the diameter of subcritical clusters.
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We investigate the disconnection time of a simple random walk in a discrete cylinder with a large finite connected base. In a recent article of A. Dembo and the author it was found that for large N the disconnection time of G(N) x Z has rough order vertical bar GN vertical bar(2), when G(N) = (Z/NZ)(d). In agreement with a conjecture by I. Benjamini, we show here that this behavior has broad generality when the bases of the discrete cylinders are large connected graphs of uniformly bounded deg...
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作者：Kesten, Harry; Sidoravicius, Vladas
作者单位：Cornell University; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider the following, problem in one-dimensional diffusion-limited agregation (DLA). At time t, we have an aggregate consisting of Z boolean AND [0, R(t)] [with R(t) a positive integer]. We also have N(i, t) particles at i, i > R(t). All these particle, perform independent continuous-time symmetric simple random Walks until the first time t' > i at Which some particle tries to jump from R(t) + l to R(t). The aggreate is then increased to the integers in [0, R(t')] = [0, R(t) + 1] [so that...
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作者：Jonasson, Johan; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We consider two dynamical variants of Dvoretzky's classical problem of random interval coverings of the unit circle, the latter having been completely solved by L. Shepp. In the first model, the centers of the intervals perform independent Brownian motions and in the second model, the positions of the intervals are updated according to independent Poisson processes where an interval of length C is updated at rate l(-a) where alpha >= 0 is a parameter. For the model with Brownian motions, a spe...
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作者：Benes, Christian
作者单位：Tufts University
摘要：We study two variants of the notion of holes formed by planar simple random walk of time duration 2n and the areas associated with them. We prove in both cases that the number of holes of area greater than A(n), where (A (n)) is an increasing sequence, is, up to a logarithmic correction term, asymptotic to n center dot A(n)(-1) for a range of large holes, thus confirming an observation by Mandelbrot. A consequence is that the largest hole has an area which is logarithmically asymptotic to n. W...
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作者：Pittel, Boris
作者单位：University System of Ohio; Ohio State University
摘要：Consider a uniformly random regular graph of a fixed degree d >= 3, with it vertices. Suppose that each edge is open (closed), with probability p(q = 1 - p), respectively. In 2004 Alon, Benjamini and Stacey proved that p* = (d - 1)(-1) is the threshold probability for emergence of a giant component in the subgraph formed by the open edges. In this paper we show that the transition window around p* has width roughly of order n(-1/3). More precisely, suppose that p = p(n) is such that omega := n...
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作者：Hwang, Hsien-Kuei; Janson, Svante
作者单位：Academia Sinica - Taiwan; Uppsala University
摘要：Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.
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作者：Antunes, Nelson; Fricker, Christine; Robert, Philippe; Tibi, Danielle
作者单位：Universidade do Algarve; Universite Paris Cite
摘要：This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit regime, that is, when the networks have some symmetry properties and when the number of nodes goes to infinity. An intriguing stability property is proved: under some conditions on the parameters, it is shown that, in the limit, several stable equilibrium p...
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作者：Merle, Mathieu
作者单位：University of British Columbia
摘要：The goal of this work is to find the asymptotics of the hitting probability of a distant point for the voter model on the integer lattice started from a single 1 at the origin. In dimensions d = 2 or 3, we obtain the precise asymptotic behavior of this probability. We use the scaling limit of the voter model started from a single 1 at the origin in terms of super-Brownian motion under its excursion measure. This invariance principle was stated by Bramson, Cox and Le Gall, as a consequence of a...
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作者：Decreusefond, Laurent; Nualart, David
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; University of Kansas
摘要：We establish a general formula for the Laplace transform of the hitting times of a Gaussian process. Some consequences are derived, and particular cases like the fractional Brownian motion are discussed.
