A zero-one law for random walks in random environments on ${\mathbb{Z}}^2$ with bounded jumps

Abstract

This paper has two main results, which are connected through the fact that the first is a key ingredient in the second. Both are extensions of results concerning directional transience of nearest-neighbor random walks in random environments to allow for bounded jumps. Zerner and Merkl proved a 0-1 law for directional transience for planar random walks in random environments. We extend the result to non-planar i.i.d. random walks in random environments on ${\mathbb{Z}}^2$ with bounded jumps. Sabot and Tournier characterized directional transience for a given direction for nearest-neighbor random walks in Dirichlet environments on ${\mathbb{Z}}^d$, $d\ge 1$. We extend this characterization to random walks in Dirichlet environments with bounded jumps.

27 pages, 6 figures

References in corpus (1)

• Random walks in random Dirichlet environment are transient in dimension $d\ge 3$