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April 2001 On a Class Of Transient Random Walks in Random Environment
Alain-Sol Sznitman
Ann. Probab. 29(2): 724-765 (April 2001). DOI: 10.1214/aop/1008956691


We introduce in this article a class of transient random walks in a random environment on $\mathbb{Z}^d$. When $d\ge 2$, these walks are ballistic and we derive a law of large numbers, a central limit theorem and large-deviation estimates. In the so-called nestling situation, large deviations in the neighborhood of the segment $[0, v]$, $v$ being the limiting velocity, are critical. They are of special interest in view of their close connection with the presence of traps in the medium, that is, pockets where a certain spectral parameter takes atypically low values.


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Alain-Sol Sznitman. "On a Class Of Transient Random Walks in Random Environment." Ann. Probab. 29 (2) 724 - 765, April 2001.


Published: April 2001
First available in Project Euclid: 21 December 2001

zbMATH: 1017.60106
MathSciNet: MR1849176
Digital Object Identifier: 10.1214/aop/1008956691

Primary: 60K40 , 82D30

Keywords: Random walk in random environment , slowdowns , traps

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 2 • April 2001
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