Electronic Journal of Probability

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

Alexis Devulder and Françoise Pène

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G52: Stable processes 60K37: Processes in random environments

random walk on randomly oriented lattices random walk in random environment random walk in random scenery functional limit theorem transience

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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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