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 criticalvalue of the decay power, above which it is almost surely recurrent and below which it is almost surely transient.
Massimo Campanino, Dimitri Petritis (2014). TYPE TRANSITION OF SIMPLE RANDOM WALKS ON RANDOMLY DIRECTED REGULAR LATTICES. JOURNAL OF APPLIED PROBABILITY, 51(4), 1065-1080.
TYPE TRANSITION OF SIMPLE RANDOM WALKS ON RANDOMLY DIRECTED REGULAR LATTICES
CAMPANINO, MASSIMO;
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 criticalvalue of the decay power, above which it is almost surely recurrent and below which it is almost surely transient.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.