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January 2003 On new examples of ballistic random walks in random environment
Alain-Sol Sznitman
Ann. Probab. 31(1): 285-322 (January 2003). DOI: 10.1214/aop/1046294312

Abstract

In this article we show that random walks in random environment on $\mathbb{Z}^d$, $d \ge3$, with transition probabilities which are $\varepsilon$-perturbations of the simple random walk and such that the expectation of the local drift has size bigger than $\varepsilon^\rho $, with $\rho< \frac{5}{2}$, when $d=3$, $\rho< 3$, when $d \ge4$, fulfill the condition (T$^\prime$) introduced by Sznitman [Prob. Theory Related Fields (2002) 122 509-544], when $\varepsilon$ is small. As a result these walks satisfy a law of large numbers with nondegenerate limiting velocity, a central limit theorem and several large deviation controls. In particular, this provides examples of ballistic random walks in random environment which do not satisfy Kalikow's condition in the terminology of Sznitman and Zerner [Ann. Probab. (1999) 27 1851-1869]. An important tool in this work is the effective criterion of Sznitman.

Citation

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Alain-Sol Sznitman. "On new examples of ballistic random walks in random environment." Ann. Probab. 31 (1) 285 - 322, January 2003. https://doi.org/10.1214/aop/1046294312

Information

Published: January 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1017.60104
MathSciNet: MR1959794
Digital Object Identifier: 10.1214/aop/1046294312

Subjects:
Primary: 60K37 , 82D30

Keywords: ballistic behavior , Random walk in random environment , small perturbations of simple random walk

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 1 • January 2003
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