Random walk in random environment in a two-dimensional stratified medium with orientations

TL;DR

This paper studies a two-dimensional random walk in a stratified medium with variable orientations and stay probabilities, proving transience and superdiffusive behavior under broad conditions, extending previous models.

Contribution

It introduces a generalized model with variable stay probabilities and orientations, demonstrating transience and superdiffusivity beyond prior fixed-probability models.

Findings

Proves transience for all fixed orientations under general conditions.

Establishes convergence in distribution with normalization.

Shows the model can be more superdiffusive than previous models.

Abstract

We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed orientations under general hypotheses. This contrasts with the model of Campanino and Petritis, in which probabilities to stay on these lines are all equal. We also establish a result of convergence in distribution for this walk with suitable normalizations under more precise assumptions. In particular, our model proves to be, in many cases, even more superdiffusive than the random walks introduced by Campanino and Petritis.