Critical RWRE on trees and tree-indexed random walks

Details Critical RWRE on trees and tree-indexed random walks Critical RWRE on trees and tree-indexed random walks

2004-04-02

arxiv.org/abs/math/0404042v1

Ann. Probab., 23, 105 - 140 (1995)

Mathematics

Probability

47 pages

Scientific paper

We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges of a tree Gamma are i.i.d.random variables whose logarithms have mean zero and finite variance. Then the resulting RWRE is transient if simple random walk on Gamma is transient, but not vice versa. We obtain general transience criteria for such walks, which are sharp for symmetric trees of polynomial growth. In order to prove these criteria, we establish results on boundary crossing by tree-indexed random walks. These results rely on comparison inequalities for percolation processes on trees and on some new estimates of boundary crossing probabilities for ordinary mean-zero finite variance random walks in one dimension, which are of independent interest.

Affiliated with

Also associated with

No associations

Rating

Critical RWRE on trees and tree-indexed random walks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Critical RWRE on trees and tree-indexed random walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical RWRE on trees and tree-indexed random walks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-287317