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.

Published in at http://dx.doi.org/10.1214/08-AOP393 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• A note on multitype branching processes with immigration in a random environment

Cited by in corpus (8)

• Large deviations for random walk in a random environment
• Limit theorems for random walks on a strip in subdiffusive regime
• Local Limit Theorems for Random Walks in a Random Environment on a Strip
• Large deviations for random walks in a random environment on a strip
• Quenched large deviations for random walk in a random environment
• Law of large numbers for random walk with unbounded jumps and BDP with bounded jumps in random environment
• Branching structure for the transient (1;R)-random walk in random environment and its applications
• Random Walks in Dirichlet Random Environments on $\mathbb{Z}$ with Bounded Jumps