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作者：Collet, P; Martínez, S; San Martín, J
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universidad de Chile
摘要：We consider a Brownian motion in a Benedicks domain with absorption at the boundary. We show ratio limit theorems for the associated heat kernel. When the hole is compact, therefore the Martin boundary is two dimensional; we obtain sharp estimates on the lifetime probabilities and we identify, in probabilistic terms, the various constants appearing in the theory.
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作者：Cassandro, M; Orlandi, E; Picco, P
作者单位：Sapienza University Rome; Roma Tre University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper we study the typical profiles of a random field Kac model. We give upper and lower bounds of the space scale where the profiles are constant. The results hold almost surely with respect to the realizations of the random field. The analysis is based on a block-spin construction, deviation techniques for the local empirical order parameters and concentration inequalities for the realizations of the random magnetic field. For the upper bound, we exhibit a scale related to the law of...
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作者：Albin, JMP; Leadbetter, MR
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We derive upper bounds for the conditional moment E{\ X \(e) \ Y = y} of a strictly alpha-stable random vector (X, Y) when alpha not equal 1 and rho less than or equal to 2 and prove weak convergence for the conditional law (X/u \ Y = u) as u --> infinity when alpha > 1. As an example of application, we derive a new result in crossing theory for ct-stable processes.
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作者：van den Berg, J; Steif, JE
作者单位：Centrum Wiskunde & Informatica (CWI); Chalmers University of Technology
摘要：We study the existence of finitary codings (also called finitary homomorphisms or finitary factor maps) from a finite-valued i.i.d. process to certain random fields. For Markov random fields we show, using ideas of Marton and Shields, that the presence of a phase transition is an obstruction for the existence of the above coding; this yields a large class of Bernoulli shifts for which no such coding exists. Conversely, we show that, for the stationary distribution of a monotone exponentially e...
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作者：Osada, H; Spohn, H
作者单位：Nagoya University; Technical University of Munich; Technical University of Munich; University of Munich
摘要：We consider Brownian motion perturbed by the exponential of an action. The action is the sum of an external, one-body potential and a two-body interaction potential which depends only on the increments. Under suitable conditions on these potentials, we establish existence and uniqueness of the corresponding Gibbs measure. We also provide an example where uniqueness fails because of a slow decay in the interaction potential.
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作者：Grigorescu, L
作者单位：McMaster University
摘要：We derive explicitly the asymptotic law of the tagged particle process in a system of interacting Brownian motions in the presence of a diffusive scaling in nonequilibrium. The interaction is local and interpolates between the totally independent case (noninteracting) and the totally reflecting case and can be viewed as the limiting local version of an interaction through a pair potential as its support shrinks to zero. We also prove the independence of two tagged particles in the limit.
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作者：Chen, X
作者单位：Northwestern University
摘要：Let {X-n}(n greater than or equal to 0) be a Harris recurrent Markov chain with state space (E, E), transition probability P(x, A) and invariant measure pi. Given a nonnegative pi-integrable function f on E, the exact asymptotic order is given for the additive functionals (n)(k=1)Sigma f(X-/e), n=1, 2,... in the forms of both weak and strong convergences. In particular, the frequency of {X-n}(n greater than or equal to 0) visiting a given set A is an element of E with 0 < pi(A) < +infinity is ...
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作者：Li, WV; Linde, W
作者单位：University of Delaware; Friedrich Schiller University of Jena
摘要：A precise link proved by Kuelbs and Li relates the small ball behavior of a Gaussian measure mu on a Banach space E with the metric entropy behavior of K mu, the unit ball of the reproducing kernel Hilbert space of mu in E. We remove the main regularity assumption imposed on the unknown function in the link. This enables the application of tools and results from functional analysis to small ball problems and leads to small ball estimates of general algebraic type as well as to new estimates fo...
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作者：Grigorescu, I
作者单位：McMaster University
摘要：It has been shown that for a system of Brownian motions with local interaction considered in a diffusive scaling, under some regularity assumptions on the initial profile, the tagged particle process converges to a diffusion. We provide a sufficient condition for granting both the existence and the uniqueness of the tagged particle process for an arbitrary initial profile.
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作者：Pisztora, A; Povel, T
作者单位：Carnegie Mellon University; Massachusetts Institute of Technology (MIT)
摘要：We consider a one-dimensional random walk (X-n)(n x N) in a random environment of zero or strictly positive drifts. We establish a full large deviation principle for X-n/n of the correct order n/(log n)(2) in the low speed regime, valid for almost every environment. This completes the large deviation picture obtained earlier by Greven and den Hollander and Gantert and Zeitouni in the case of zero and positive drifts. The proof uses coarse graining along with concentration of measure techniques.
