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2016 Zero-one law for directional transience of one-dimensional random walks in dynamic random environments
Tal Orenshtein, Renato Soares dos Santos
Electron. Commun. Probab. 21: 1-11 (2016). DOI: 10.1214/16-ECP4426

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. An immediate consequence is the recurrence of models that are symmetric with respect to reflection through the origin.

Citation

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Tal Orenshtein. Renato Soares dos Santos. "Zero-one law for directional transience of one-dimensional random walks in dynamic random environments." Electron. Commun. Probab. 21 1 - 11, 2016. https://doi.org/10.1214/16-ECP4426

Information

Received: 13 July 2015; Accepted: 26 January 2016; Published: 2016
First available in Project Euclid: 19 February 2016

zbMATH: 1338.60102
MathSciNet: MR3485384
Digital Object Identifier: 10.1214/16-ECP4426

Subjects:
Primary: 60F20, 60K37
Secondary: 82B41, 82C44

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