Random walks of infinite moment on free semigroups

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].

Random walks on semaphore codes and delay de Bruijn semigroups

Random Walks Driven by Low Moment Measures

We study the decay of convolution powers of probability measures without second moment but satisfying some weaker finite moment condition. For any locally compact unimodular group G and any positive function :G→ [0,+∞], we introduce a function G, which describes the fastest possible decay of n → φ(2n)(e) when φ is a symmetric continuous probability density such that ∫ φ is finite. We estimate G...

Infinite–dimensional Diffusions as Limits of Random Walks on Partitions

The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group S∞. This problem leads to a family {Pz} of probability measures, the z–measures, which depend on the complex parameter z ∈ C. The z–measures live on the Thoma simplex, an infinite–dimensional compact space Ω which is a kind of dual object to the group S∞. The aim of the paper...

Boundaries and random walks on finitely generated infinite groups

We prove that almost every path of a random walk on a finitely generated non-amenable group converges in the compactification of the group introduced by W.J. Floyd. In fact, we consider the more general setting of ergodic cocycles of some semigroup of 1-Lipschitz maps of a complete metric space with a boundary constructed following Gromov. We obtain in addition that when the Floyd boundary of a...