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Rate of escape of random walks on free products

Published online by Cambridge University Press:  09 April 2009

Lorenz A. Gilch
Affiliation:
University of Technology GrazInstitut fur Mathematische Strukturtheorie (Math. C)Steyrergasse 30 A-8010GrazAustriagilch@TUGraz.at
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Abstract

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Suppose we are given the free product V of a finite family of finite or countable sets (Vi)i∈∮ and probability measures on each Vi, which govern random walks on it. We consider a transient random walk on the free product arising naturally from the random walks on the Vi. We prove the existence of the rate of escape with respect to the block length, that is, the speed at which the random walk escapes to infinity, and furthermore we compute formulae for it. For this purpose, we present three different techniques providing three different, equivalent formulae.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

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