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作者：Steele, JM; Zhang, Y
作者单位：University of Pennsylvania; University of Colorado System; University of Colorado at Colorado Springs
摘要：We study the paths of minimal cost for first-passage percolation in two dimensions and obtain an exponential bound on the tail probability of the ratio of the lengths of the shortest and longest of these. This inequality permits us to answer a long-standing question of Hammersley and Welsh on the shift differentiability of the time constant. Specifically, we show that for subcritical Bernoulli percolation the time constant is not shift differentiable when p is close to one-half.
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作者：Alabert, A; Ferrante, M
作者单位：Autonomous University of Barcelona; University of Padua
摘要：We consider linear nth order stochastic differential equations on [0, 1], with linear boundary conditions supported by a finite subset of [0, 1]. We study some features of the solution to these problems, and especially its conditional independence properties of Markovian type.
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作者：Owhadi, H
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper is concerned with the asymptotic behavior of solutions of stochastic differential equations dy(t) = domega(t) - delV(y(t))dt, y(0) = 0. When d = 1 and V is not periodic but obtained as a superposition of an infinite number of periodic potentials with geometrically increasing periods [V(x) = Sigma(k=0)(infinity) U-k(x/R-k), where U-k are smooth functions of period 1, U-k(0) = 0, and R-k grows exponentially fast with k] we can show that yt has an anomalous slow behavior and we obtain ...
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作者：Erschler, A
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：In this paper we consider drift and entropy growth for symmetric finitary random walks on finitely generated groups. We construct examples of various intermediate asymptotics of the drift for such random walks. We establish general inequalities which connect drift, entropy and exponential growth rate of groups. Then we apply these inequalities to get estimates for entropy in particular examples.
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作者：Taylor, JE; Adler, RJ
作者单位：Stanford University; Technion Israel Institute of Technology
摘要：We are interested in the geometric properties of real-valued Gaussian random fields defined on manifolds. Our manifolds, M, are of class C-3 and the random fields f are smooth. Our interest in these fields focuses on their excursion sets, f(-1)[u, + infinity), and their geometric properties. Specifically, we derive the expected Euler characteristic E[chi(f(-1)[u, + infinity))] of an excursion set of a smooth Gaussian random field. Part of the motivation for this comes from the fact that E[chi(...
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作者：Sznitman, AS
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this article we show that random walks in random environment on Z(d), d greater than or equal to 3, with transition probabilities which are epsilon-perturbations of the simple random walk and such that the expectation of the local drift has size bigger than epsilon(rho), with rho < 5/2, when d = 3, rho < 3, when d greater than or equal to 4, fulfill the condition (T') introduced by Sznitman [Prob. Theory Related Fields (2002) 122 509-544], when E is small. As a result these walks satisfy a ...
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作者：Jing, BY; Shao, QM; Wang, QY
作者单位：Hong Kong University of Science & Technology; University of Oregon; National University of Singapore; National University of Singapore; University of Sydney
摘要：Let X-1, X-2,... be independent random variables with zero means and finite variances. It is well known that a finite exponential moment assumption is necessary for a Cramer-type large deviation result for the standardized partial sums. In this paper, we show that a Cramer-type large deviation theorem holds for self-normalized sums only under a finite (2 + delta)th moment, 0 < delta less than or equal to 1. In particular, we show P(S-n/ V-n greater than or equal to x) = (1 - Phi(x))(1 + O(1)(1...
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作者：Duquesne, T
作者单位：Universite Paris Saclay
摘要：In this work, we study asymptotics of the genealogy of Galton-Watson processes conditioned on the total progeny. We consider a fixed, aperiodic and critical offspring distribution such that the rescaled Galton-Watson processes converges to a continuous-state branching process (CSBP) with a stable. branching mechanism of index a e (1, 2]. We code the genealogy by two different processes: the contour process and the height process that Le Gall and Le Jan recently introduced [21, 22]. We show tha...
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作者：Hösel, V; Lasser, R
作者单位：Helmholtz Association; Helmholtz-Center Munich - German Research Center for Environmental Health
摘要：We investigate random sequences (X(n))(nis an element ofN0) with spectral representation based on certain orthogonal polynomials, that is, random sequences that are weakly stationary with respect to polynomial hypergroups. We present various situations where one meets this kind of sequence. The main topic is on the one-step prediction. In particular, it is examined when the mean-squared error tends to zero. For many cases we present a complete solution for the problem of (X(n))(nis an element ...
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作者：De La Peña, VH; Ibragimov, R; Sharakhmetov, S
作者单位：Columbia University; Yale University; Tashkent State University of Economics
摘要：In this paper we present a study of the problem of approximating the expectations of functions of statistics in independent and dependent random variables in terms of the expectations of functions of the component random variables. We present results providing sharp analogues of the Burkholder-Rosenthal inequalities and related estimates for the expectations of functions of sums of dependent nonnegative r.v.'s and conditionally symmetric martingale differences with bounded conditional moments ...
