Asymptotic Entropy of Random Walks on Free Products

Details Asymptotic Entropy of Random Walks on Free Products Asymptotic Entropy of Random Walks on Free Products

2010-05-26

arxiv.org/abs/1005.4778v4

Mathematics

Probability

31 pages, 1 figure; final version of accepted paper

Scientific paper

Suppose we are given the free product V of a finite family of finite or countable sets. We consider a transient random walk on the free product arising naturally from a convex combination of random walks on the free factors. We prove the existence of the asymptotic entropy and present three different, equivalent formulas, which are derived by three different techniques. In particular, we will show that the entropy is the rate of escape with respect to the Greenian metric. Moreover, we link asymptotic entropy with the rate of escape and volume growth resulting in two inequalities.

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