Entropy of random walk range on uniformly transient and on uniformly recurrent graphs

Details Entropy of random walk range on uniformly transient and on uniformly recurrent graphs Entropy of random walk range on uniformly transient and on uniformly recurrent graphs

2010-01-03

arxiv.org/abs/1001.0355v2

Electronic Journal of Probability 2010, Vol. 15, 1143-1160

Mathematics

Probability

17 pages, 2 figures

Scientific paper

We study the entropy of the distribution of the set R_n of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of R_n if the graph is uniformly transient, and sublinearly in the expected size if the graph is uniformly recurrent with subexponential volume growth. This in particular answers a question asked by Benjamini, Kozma, Yadin and Yehudayoff (arXiv:0903.3179v1).

Affiliated with

Also associated with

No associations

Rating

Entropy of random walk range on uniformly transient and on uniformly recurrent graphs 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 Entropy of random walk range on uniformly transient and on uniformly recurrent graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entropy of random walk range on uniformly transient and on uniformly recurrent graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-222763