## Electronic Communications in Probability

### Random walk in a stratified independent random environment

Brémont Julien

#### 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
Accepted: 21 June 2019
First available in Project Euclid: 5 September 2019

https://projecteuclid.org/euclid.ecp/1567649074

Digital Object Identifier
doi:10.1214/19-ECP252

#### 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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