Spectral properties of a class of random walks on locally finite groups Auteur(s): Bendikov Alexander, Bobikau Barbara, Pittet Christophe
Ref HAL: hal-01304985_v1 Ref Arxiv: 1102.1952 DOI: 10.4171/GGD/206 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e.g. the infinite symmetric group. On locally finite groups, the random walks under consideration are driven by infinite divisible distributions. This allows us to embed our random walks into continuous time L\'evy processes whose heat kernels have shapes similar to the ones of alpha-stable processes. We obtain examples of fast/slow decays of return probabilities, a recurrence criterion, exact values and estimates of isospectral profiles and spectral distributions, formulae and estimates for the escape rates and for heat kernels. Commentaires: 62 pages, 1 figure, 2 tables |