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Pré-Publication, Document De Travail Année : 2012

Type transition of simple random walks on randomly directed regular lattices

Résumé

Simple random walks on a partially directed version of $\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\mathbb{Z}^2$ can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function, the perturbation probability decays according to a power law in the absolute value of the ordinate. We study the type of the simple random walk, i.e.\ its being recurrent or transient, and show that there exists a critical value of the decay power, above which the walk is almost surely recurrent and below which is almost surely transient.
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Dates et versions

hal-00690677 , version 1 (24-04-2012)
hal-00690677 , version 2 (18-03-2014)

Identifiants

  • HAL Id : hal-00690677 , version 1

Citer

Massimo Campanino, Dimitri Petritis. Type transition of simple random walks on randomly directed regular lattices. 2012. ⟨hal-00690677v1⟩
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