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

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Date
2015
Volume
2151
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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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.

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Keywords
Random walk, dynamic random environment, zero-one law, directional transience, recurrence
Citation
Orenshtein, T., & Santos, R. S. d. (2015). Zero-one law for directional transience of one-dimensional random walks in dynamic random environments (Vol. 2151). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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