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作者：Martin, JB
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We consider directed first-passage and last-passage percolation on the nonnegative lattice Z(+)(d), d greater than or equal to 2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits g(x) = lim(n-->infinity)n(-1)T([nx]) exist and are constant a.s. for x is an element of R-+(d), where T(z) is the passage time from the origin to the vertex z is an element of Z(+)(d). We show that this shape function g is continuous on R-+(d), ...
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作者：Biskup, M
作者单位：University of California System; University of California Los Angeles
摘要：We consider the (unoriented) long-range percolation on Z(d) in dimensions d greater than or equal to 1, where distinct sites x,y is an element of Z(d) get connected with probability p(xy) is an element of [0, 1]. Assuming p(xy) = \x - y\(-s+o(1)) as \x - y\ --> infinity, where s > 0 and \ (.) \ is a norm distance on Z(d), and supposing that the resulting random graph contains an infinite connected component Cinfinity, we let D(x, y) be the graph distance between x and y measured on Cinfinity. ...
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作者：Fukushima, M; He, P; Ying, JG
作者单位：Kansai University; Shanghai University of Finance & Economics; Fudan University
摘要：We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using the approach of time change of Markov processes.
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作者：Kösters, H
作者单位：University of Munster
摘要：Let X-1, X-2,... be a sequence of [0, 1]-valued i.i.d. random variables, let c greater than or equal to 0 be a sampling cost for each observation and let Y-i = X-i - ic, i = 1, 2,.... For n = 1, 2,..., let M(Y-1,..., Y-n) = E(max(1 less than or equal to i) (less than or equal to n) Y-i) and V(Y-1,..., Y-n) sup(tauis an element ofC)(n) E(Y-tau), where C-n denotes the set of all stopping rules for Y-1,..., Y-n. Sharp upper bounds for the difference M(Y-1,..., Y-n) -V (Y-1,..., Y-n) are given und...
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作者：Sabot, C
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
摘要：We consider random walks in a random environment of the type p(0) + gammaxiz, where p(0) denotes the transition probabilities of a stationary random walk on Z(d), to nearest neighbors, and xi(Z) is an i.i.d. random perturbation. We give an explicit expansion, for small gamma, of the asymptotic speed of the random walk under the annealed law, up to order 2. As an application, we construct, in dimension d greater than or equal to 2, a walk which goes faster than the stationary walk under the mea...
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作者：Chen, DY; Peres, Y; Pete, G
作者单位：Peking University; University of California System; University of California Berkeley
摘要：Benjamini, Lyons and Schramm [Random Walks and Discrete Potential Theory (1999) 56-84] considered properties of an infinite graph G, and the simple random walk on it, that are preserved by random perturbations. In this paper we solve several problems raised by those authors. The anchored expansion constant is a variant of the Cheeger constant; its positivity implies positive lower speed for the simple random walk, as shown by Virag [Geom. Funct. Anal. 10 (2000) 1588-1605]. We prove that if G h...
