Range of random walks on free products

Rate of Escape of Random Walks on Free Products

Suppose we are given the free product V of a finite family of finite or countable sets (Vi)i∈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 e...

Random walks on free products of cyclic groups

Let G be a free product of a finite family of finite groups, with the set of generators being formed by the union of the finite groups. We consider a transient nearest-neighbor random walk on G. We give a new proof of the fact that the harmonic measure is a special Markovian measure entirely determined by a finite set of polynomial equations. We show that in several simple cases of interest, th...

Asymptotic Entropy of Random Walks on Free Products

Suppose we are given the free product V of a finite family of finite or countable sets. We consider a transient random walk on the free product arising naturally from a convex combination of random walks on the free factors. We prove the existence of the asymptotic entropy and present three different, equivalent formulas, which are derived by three different techniques. In particular, we will s...

Random walks, random configurations, and horocyclic products

Random Walks on Infinite Free Products and Infinite Algebraic Systems of Generating Functions

The return probabilities of certain random walks on infinite free products of finite groups are shown to obey a Local Limit Theorem of the same type as for nearestneighbor random walks on finite free products. The analysis is based on an infinitedimensional extension of a technique for studying finite algebraic systems of generating functions introduced by the author in [12] and [13].