Open Access
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


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.


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

Primary: 60F17
Secondary: 60G52 , 60K37

Keywords: Functional limit theorem , Random walk in random environment , Random walk in random scenery , random walk on randomly oriented lattices , transience

Vol.18 • 2013
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