Rate of Escape on Free Products

2007/08/28 by Gilch, Lorenz
#60B15 (Secondary) #60G50 (Primary) 20E06 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0708.3763

Abstract

Suppose we are given the free product V of a finite family of finite or countable sets (V_i)_i\inI 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 formulas for it. For this purpose, we present three different techniques providing three different, equivalent formulas.

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