Asymptotic entropy and green speed for random walks on countable groups

Details Asymptotic entropy and green speed for random walks on countable groups Asymptotic entropy and green speed for random walks on countable groups

2006-07-19

arxiv.org/abs/math/0607467v4

Annals of Probability 2008, Vol. 36, No. 3, 1134-1152

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP356 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP356

We study asymptotic properties of the Green metric associated with transient random walks on countable groups. We prove that the rate of escape of the random walk computed in the Green metric equals its asymptotic entropy. The proof relies on integral representations of both quantities with the extended Martin kernel. In the case of finitely generated groups, where this result is known (Benjamini and Peres [Probab. Theory Related Fields 98 (1994) 91--112]), we give an alternative proof relying on a version of the so-called fundamental inequality (relating the rate of escape, the entropy and the logarithmic volume growth) extended to random walks with unbounded support.

Affiliated with

Also associated with

No associations

Rating

Asymptotic entropy and green speed for random walks on countable groups 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 Asymptotic entropy and green speed for random walks on countable groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic entropy and green speed for random walks on countable groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-625845