Ergodic properties of boundary actions

Tatiana Smirnova-Nagnibeda of the Royal Institute of Technology in Stockholm

We study the action of a subgroup H of a free group F on the Poisson boundary of the simple random walk on F. By methods of combinatorial group theory, we identify the conservative and dissipative parts of the action. Necessary and sufficient conditions of conservativity of the action of H on the boundary of F are given in terms of geometry of the quotient (Schreier graph) F/H. This is a joint work with R. Grigorhcuk and V. Kaimanovich.