Electronic Communications in Probability

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

Tal Orenshtein and Renato Soares dos Santos

Full-text: Open access

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.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 15, 11 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1455897057

Digital Object Identifier
doi:10.1214/16-ECP4426

Mathematical Reviews number (MathSciNet)
MR3485384

Zentralblatt MATH identifier
1338.60102

Subjects
Primary: 60F20: Zero-one laws 60K37: Processes in random environments
Secondary: 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41] 82C44: Dynamics of disordered systems (random Ising systems, etc.)

Keywords
random walk dynamic random environment zero-one law transience recurrence

Rights
Creative Commons Attribution 4.0 International License.

Citation

Orenshtein, Tal; Soares dos Santos, Renato. Zero-one law for directional transience of one-dimensional random walks in dynamic random environments. Electron. Commun. Probab. 21 (2016), paper no. 15, 11 pp. doi:10.1214/16-ECP4426. https://projecteuclid.org/euclid.ecp/1455897057


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