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Rate of escape of random walks on free products

Part of: Stochastic processes Probability theory on algebraic and topological structures Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Lorenz A. Gilch
Lorenz A. Gilch
Affiliation:
University of Technology GrazInstitut fur Mathematische Strukturtheorie (Math. C)Steyrergasse 30 [email protected]
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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.

Keywords

random walksfree productsrate of escape

MSC classification

Secondary: 60G50: Sums of independent random variables; random walks 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 1 , August 2007 , pp. 31 - 54
Copyright
Copyright © Australian Mathematical Society 2007

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