Random walk in a stratified independent random environment

Abstract

We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results previously established in [2]. The random walk is first shown to be transient in dimension at least three. Focusing on dimension two, we provide sharp sufficient conditions for either recurrence or transience. We determine the critical scale of the local drift along the strata, corresponding to the frontier between the two regimes.