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Random walk in random environment in a two-dimensional stratified medium with orientations. (English) Zbl 1283.60058

Summary: 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 i.i.d. 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 M. Campanino and D. Petritis [Markov Process. Relat. Fields 9, No. 3, 391–412 (2003; Zbl 1057.60069)].

MSC:

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

Citations:

Zbl 1057.60069
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