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December 2014 Type transition of simple random walks on randomly directed regular lattices
Massimo Campanino, Dimitri Petritis
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J. Appl. Probab. 51(4): 1065-1080 (December 2014).

Abstract

Simple random walks on a partially directed version of Z2 are considered. More precisely, vertical edges between neighbouring vertices of Z2 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 simple random walk that is recurrent or transient, and show that there exists a critical value of the decay power, above which it is almost surely recurrent and below which it is almost surely transient.

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Massimo Campanino. Dimitri Petritis. "Type transition of simple random walks on randomly directed regular lattices." J. Appl. Probab. 51 (4) 1065 - 1080, December 2014.

Information

Published: December 2014
First available in Project Euclid: 20 January 2015

zbMATH: 1310.60048
MathSciNet: MR3301289

Subjects:
Primary: 60J10
Secondary: 60K15

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 4 • December 2014
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