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作者：Ignatiouk-Robert, Irina
作者单位：CY Cergy Paris Universite
摘要：The complete representation of the Martin compactification for reflected random walks on a half-space Z(d) x N is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the radial compactification obtained by Ney and Spitzer for the homogeneous random walks in Zd : convergence of a sequence of points z(n) is an element of Z(d-1) x N to a point of on the Martin boundary does not imply convergence of the sequence z(n)/vertical bar z(n)vertical bar on the un...
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作者：van der Hofstad, Remco; Holmes, Mark
作者单位：Eindhoven University of Technology; University of Auckland
摘要：We prove that the drift theta(d, beta) for excited random walk in dimension d is monotone in the excitement parameter beta is an element of [0, 1], when d is sufficiently large. We give an explicit criterion for monotonicity involving random walk Green's functions, and use rigorous numerical upper bounds provided by Hara (Private communication, 2007) to verify the criterion for d >= 9.
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作者：Ding, Jian; Lubetzky, Eyal; Peres, Yuval
作者单位：Microsoft; University of California System; University of California Berkeley
摘要：The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. Diaconis [Proc Natl Acad Sci USA 93(4): 1659-1664, 1996] surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite ergodic Markov chains. Peres [American Institute of Mathematics (AIM) Research Workshop, Palo Alto. http://www.aimath.org/WWN/mixingtimes, 2004] noted that a necessary condition for cutoff in a family of reversible chain...
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作者：Mossel, Elchanan; Sly, Allan
作者单位：University of California System; University of California Berkeley
摘要：Gibbs sampling also known as Glauber dynamics is a popular technique for sampling high dimensional distributions defined on graphs. Of special interest is the behavior of Gibbs sampling on the Erdos-Renyi random graph G(n, d/n), where each edge is chosen independently with probability d/n and d is fixed. While the average degree in G(n, d/n) is d(1-o(1)), it contains many nodes of degree of order (log n)/(log log n). The existence of nodes of almost logarithmic degrees implies that for many na...
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作者：Kifer, Yuri
作者单位：Hebrew University of Jerusalem
摘要：The polynomial ergodic theorem ( PET) which appeared in Bergelson (Ergod. Th. Dynam. Sys. 7, 337-349, 1987) and attracted substantial attention in ergodic theory studies the limits of expressions having the form 1/N Sigma(N)(n=1) T-q1(n) f(1) ... T-ql(n) f(l) where T is a weakly mixing measure preserving transformation, f(i)'s are bounded measurable functions and q(i)'s are polynomials taking on integer values on the integers. Motivated partially by this result we obtain a central limit theore...
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作者：Cheliotis, Dimitris; Virag, Balint
作者单位：Eindhoven University of Technology; University of Toronto
摘要：We consider random walk on a mildly random environment on finite transitive d-regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph changes from a regular tree to the integers, the noise becomes localized.
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作者：Freidlin, M.; Koralov, L.
作者单位：University System of Maryland; University of Maryland College Park
摘要：In this paper, we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes. In particular, we discuss the exit problem and metastability for the processes corresponding to quasi-linear initial-boundary value problems.
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作者：van der Hofstad, Remco; Luczak, Malwina J.
作者单位：University of London; London School Economics & Political Science; Eindhoven University of Technology
摘要：We study random subgraphs of the 2-dimensional Hamming graph H(2, n), which is the Cartesian product of two complete graphs on n vertices. Let p be the edge probability, and write p = (1 + epsilon)/(2(n - 1)) for some epsilon is an element of R. In Borgs et al. (Random Struct Alg 27:137-184, 2005; Ann Probab 33:1886-1944, 2005), the size of the largest connected component was estimated precisely for a large class of graphs including H(2, n) for e <= Lambda V-1/3, where Lambda > 0 is a constant...
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作者：Fribergh, Alexander; Gantert, Nina; Popov, Serguei
作者单位：University of Munster; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universidade de Sao Paulo
摘要：We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order ...
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作者：Delbaen, Freddy; Tang, Shanjian
作者单位：Fudan University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations in R-p (p is an element of [1, infinity)) and backward stochastic differential equations (BSDEs) in R-p x H-p (p is an element of (1, infinity)) and in R-infinity x (L-infinity) over bar (BMO), with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman's inequality plays a crucial role in the development of our theory, which seems to be new. Se...
