Alexander I. Bufetov: Cesaro convergence of spherical averages for measure-preserving actions of word-hyperbolic groups

Cesaro convergence of spherical averages is proven for measure-preserving actions of Markov semigroups and groups. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of spherical averages with respect to any symmetric set of generators. The proof is based on the method of Markov operators. The talk is based on the joint work with Mikhail Khristoforov and Alexey Klimenko, to appear in IMRN, available as a preprint arXiv:1101.5459.