Law of large numbers for a finite-range random walk in a dynamic random environment with nonuniform mixing

Abstract

In this paper, we study random walks evolving on Z in a dynamic random environment that we assume to have time correlations that decrease polynomially fast. We show a law of large numbers by generalizing methods already used for the nearest-neighbor framework to the finite-range one. This requires some new ideas to get around the absence of a monotonicity property that was crucial in the proof for the nearest-neighbour case. Our proof works both in discrete and continuous time.

30 pages, 5 figures

References in corpus (4)

• An almost sure invariance principle for random walks in a space-time random environment
• Reconstructing a Random Potential from its Random Walks
• Limit laws for transient random walks in random environment on $\z$
• Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing

Cited by in corpus (1)

• Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing