## The Annals of Probability

### On a Class Of Transient Random Walks in Random Environment

Alain­Sol Sznitman

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 29, Number 2 (2001), 724-765.

Dates
First available in Project Euclid: 21 December 2001

https://projecteuclid.org/euclid.aop/1008956691

Digital Object Identifier
doi:10.1214/aop/1008956691

Mathematical Reviews number (MathSciNet)
MR1849176

Zentralblatt MATH identifier
1017.60106

#### Citation

Sznitman, Alain­Sol. On a Class Of Transient Random Walks in Random Environment. Ann. Probab. 29 (2001), no. 2, 724--765. doi:10.1214/aop/1008956691. https://projecteuclid.org/euclid.aop/1008956691

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