Electronic Communications in Probability

Random walk in a stratified independent random environment

Brémont Julien

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Abstract

We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results previously established in [2]. The random walk is first shown to be transient in dimension at least three. Focusing on dimension two, we provide sharp sufficient conditions for either recurrence or transience. We determine the critical scale of the local drift along the strata, corresponding to the frontier between the two regimes.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 47, 15 pp.

Dates
Received: 14 November 2018
Accepted: 21 June 2019
First available in Project Euclid: 5 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1567649074

Digital Object Identifier
doi:10.1214/19-ECP252

Subjects
Primary: 60G17: Sample path properties 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K37: Processes in random environments

Keywords
Markov chain recurrence stratification random environment independence

Rights
Creative Commons Attribution 4.0 International License.

Citation

Julien, Brémont. Random walk in a stratified independent random environment. Electron. Commun. Probab. 24 (2019), paper no. 47, 15 pp. doi:10.1214/19-ECP252. https://projecteuclid.org/euclid.ecp/1567649074


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