J. Aust. Math. Soc. 83 (2007), no. 1, pp. 31–54.

Rate of escape of random walks on free products

Lorenz A. Gilch
University of Technology Graz
Institut für Mathematische Strukturtheorie (Math. C)
Steyrergasse 30
A-8010 Graz
Austria
gilch@TUGraz.at
Received 23 June 2005; revised 24 April 2006
Communicated by V. Stefanov

Abstract

Suppose we are given the free product V of a finite family of finite or countable sets (V_i)_{i\in \mathcal {I}} and probability measures on each V_i, which govern random walks on it. We consider a transient random walk on the free product arising naturally from the random walks on the V_i. 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.

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2000 Mathematics Subject Classification: primary 60G50; secondary 20E06, 60B15
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2354??? Z'blatt-MATH: pre05231331

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