 1239 Massimo Campanino and Dimitri Petritis
 Type transition of simple random walks on randomly directed regular lattices
(448K, pdf)
Apr 24, 12

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

Abstract. 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 oneway. 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.
 Files:
1239.src(
1239.keywords ,
rwroldecayingrandomness.pdf.mm )