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

Author

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  • den Hollander, F.
  • dos Santos, R.
  • Sidoravicius, V.

Abstract

We prove a law of large numbers for a class of Zd-valued random walks in dynamic random environments, including non-elliptic examples. We assume for the random environment a mixing property called 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 (2004) [5] for static random environments and adapted by Avena et al. (2011) [2] to dynamic random environments. A number of one-dimensional examples are given. In some cases, the sign of the speed can be determined.

Suggested Citation

  • den Hollander, F. & dos Santos, R. & Sidoravicius, V., 2013. "Law of large numbers for non-elliptic random walks in dynamic random environments," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 156-190.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:156-190
    DOI: 10.1016/j.spa.2012.09.002
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    Cited by:

    1. Avena, L. & Blondel, O. & Faggionato, A., 2018. "Analysis of random walks in dynamic random environments via L2-perturbations," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3490-3530.

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