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

W.Th.F. Hollander, den, R. Santos, dos, V. Sidoravicius

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Abstract

In this paper we prove a law of large numbers for a general class of Zd-valued random walks in dynamic random environments, including examples that are non-elliptic. We assume that the random environment has a certain space-time mixing property, which we call conditional cone-mixing, and that the random walk has a tendency to stay inside wide enough space-time cones. The proof is based on a generalization of the regeneration scheme developed by Comets and Zeitouni [5] for static random environments, which was recently adapted by Avena, den Hollander and Redig [1] to dynamic random environments. We exhibit a number of one-dimensional examples to which our law of large numbers applies. For some of these examples the sign of the speed can be determined.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages34
Publication statusPublished - 2011

Publication series

NameReport Eurandom
Volume2011012
ISSN (Print)1389-2355

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