Law of large numbers for non-elliptic random walks in dynamic random environments

Abstract

We prove a law of large numbers for a class of ${\mathbb{Z}}^d$-valued random walks in dynamic random environments, including non-elliptic examples. We assume for the random environment a mixing property called \emph{conditional cone-mixing} and that the random walk tends to stay inside wide enough space-time cones. The proof is based on a generalization of a regeneration scheme developed by Comets and Zeitouni for static random environments and adapted by Avena, den Hollander and Redig to dynamic random environments. A number of one-dimensional examples are given. In some cases, the sign of the speed can be determined.

36 pages, 4 figures

References in corpus (2)

• On the Critical Behavior at the Lower Phase Transition of the Contact Process
• Large deviation principle for one-dimensional random walk in dynamic random environment: attractive spin-flips and simple symmetric exclusion

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