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2011 Asymptotic Entropy of Random Walks on Free Products
Lorenz Gilch
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Electron. J. Probab. 16: 76-105 (2011). DOI: 10.1214/EJP.v16-841

Abstract

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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Lorenz Gilch. "Asymptotic Entropy of Random Walks on Free Products." Electron. J. Probab. 16 76 - 105, 2011. https://doi.org/10.1214/EJP.v16-841

Information

Accepted: 2 January 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1225.60126
MathSciNet: MR2749773
Digital Object Identifier: 10.1214/EJP.v16-841

Subjects:
Primary: 60J10
Secondary: 20E06, 28D20

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Vol.16 • 2011
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