## Electronic Journal of Probability

### Random walk in random environment in a two-dimensional stratified medium with orientations

#### Abstract

We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed orientations under general hypotheses. This contrasts with the model of Campanino and Petritis, in which probabilities to stay on these lines are all equal. We also establish a result of convergence in distribution for this walk with suitable normalizations under more precise assumptions. In particular, our model proves to be, in many cases, even more superdiffusive than the random walks introduced by Campanino and Petritis.

#### Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 18, 23 pp.

Dates
Accepted: 29 January 2013
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465064243

Digital Object Identifier
doi:10.1214/EJP.v18-2459

Mathematical Reviews number (MathSciNet)
MR3035746

Zentralblatt MATH identifier
1283.60058

Rights

#### Citation

Devulder, Alexis; Pène, Françoise. Random walk in random environment in a two-dimensional stratified medium with orientations. Electron. J. Probab. 18 (2013), paper no. 18, 23 pp. doi:10.1214/EJP.v18-2459. https://projecteuclid.org/euclid.ejp/1465064243

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