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 GrazInstitut für Mathematische Strukturtheorie (Math. C)Steyrergasse 30A-8010 GrazAustriagilch@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.

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

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