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June 2013 Quenched limits for the fluctuations of transient random walks in random environment on $\mathbb{Z}$
Nathanaël Enriquez, Christophe Sabot, Laurent Tournier, Olivier Zindy
Ann. Appl. Probab. 23(3): 1148-1187 (June 2013). DOI: 10.1214/12-AAP867

Abstract

We consider transient nearest-neighbor random walks in random environment on $\mathbb{Z}$. For a set of environments whose probability is converging to 1 as time goes to infinity, we describe the fluctuations of the hitting time of a level $n$, around its mean, in terms of an explicit function of the environment. Moreover, their limiting law is described using a Poisson point process whose intensity is computed. This result can be considered as the quenched analog of the classical result of Kesten, Kozlov and Spitzer [Compositio Math. 30 (1975) 145–168].

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Nathanaël Enriquez. Christophe Sabot. Laurent Tournier. Olivier Zindy. "Quenched limits for the fluctuations of transient random walks in random environment on $\mathbb{Z}$." Ann. Appl. Probab. 23 (3) 1148 - 1187, June 2013. https://doi.org/10.1214/12-AAP867

Information

Published: June 2013
First available in Project Euclid: 7 March 2013

zbMATH: 1279.60126
MathSciNet: MR3076681
Digital Object Identifier: 10.1214/12-AAP867

Subjects:
Primary: 60F05 , 60K37 , 82B41
Secondary: 60E07 , 60E10

Keywords: Beta distributions , Fluctuation theory for random walks , Poisson point process , quenched distribution , Random walk in random environment

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.23 • No. 3 • June 2013
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