WIAS Preprint No. 2151, (2015)

Zero-one law for directional transience of one-dimensional random walks in dynamic random environments



Authors

  • Orenshtein, Tal
  • Soares dos Santos, Renato

2010 Mathematics Subject Classification

  • 60F20 60K37 82B41 82C44

Keywords

  • random walk, dynamic random environment, zero-one law, directional transience, recurrence

Abstract

We prove the trichotomy between transience to the right, transience to the left and recurrence of one-dimensional nearest-neighbour random walks in dynamic random environments under fairly general assumptions, namely: stationarity under space-time translations, ergodicity under spatial translations, and a mild ellipticity condition. In particular, the result applies to general uniformly elliptic models and also to a large class of non-uniformly elliptic cases that are i.i.d. in space and Markovian in time.

Appeared in

  • Electron. Comm. Probab., 21 (2016), pp. 15/1--15/11.

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