Transient random walks on a strip in a random environment

Abstract

We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429–447]. We derive a strong law of large numbers for the random walks in a general ergodic setup and obtain an annealed central limit theorem in the case of uniformly mixing environments. In addition, we prove that the law of the “environment viewed from the position of the walker” converges to a limiting distribution if the environment is an i.i.d. sequence.