On a Class Of Transient Random Walks in Random Environment

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.