Collisions of Random Walks

Details Collisions of Random Walks Collisions of Random Walks

2010-03-16

arxiv.org/abs/1003.3255v1

Mathematics

Probability

31 pages, 4 figures

Scientific paper

A recurrent graph $G$ has the infinite collision property if two independent random walks on $G$, started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton-Watson tree with finite variance conditioned to survive, the incipient infinite cluster in $\Z^d$ with $d \ge 19$ and the uniform spanning tree in $\Z^2$ all have the infinite collision property. For power-law combs and spherically symmetric trees, we determine precisely the phase boundary for the infinite collision property.

Affiliated with

Also associated with

No associations

Rating

Collisions of 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 Collisions of Random Walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Collisions of Random Walks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-233223