4 research outputs found
Random walk in random environment in a two-dimensional stratified medium with orientations
We consider a model of random walk in with (fixed or random)
orientation of the horizontal lines (layers) and with non constant iid
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 Campanino and Petritis.Comment: 23 pages, 1 figur
TYPE TRANSITION OF SIMPLE RANDOM WALKS ON RANDOMLY DIRECTED REGULAR LATTICES
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