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2013 Random walk in random environment in a two-dimensional stratified medium with orientations
Alexis Devulder, Françoise Pène
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Electron. J. Probab. 18: 1-23 (2013). DOI: 10.1214/EJP.v18-2459

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.

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Alexis Devulder. Françoise Pène. "Random walk in random environment in a two-dimensional stratified medium with orientations." Electron. J. Probab. 18 1 - 23, 2013. https://doi.org/10.1214/EJP.v18-2459

Information

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

zbMATH: 1283.60058
MathSciNet: MR3035746
Digital Object Identifier: 10.1214/EJP.v18-2459

Subjects:
Primary: 60F17
Secondary: 60G52, 60K37

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Vol.18 • 2013
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