Ergodic theorem for Markov groups

I will speak about ergodic theorems for actions of Markov (semi)groups. A definition of Markov semigroup was given by Cannon and Gromov, who discovered that any hyperbolic group is Markov. The first talk is devoted to ergodic theorems for the simplest examples of Markov semigroups, that is, free semigroup and free group. Also I will show that the same approach works for some subclass of Markov groups. On the second talk an ergodic theorem for arbitrary Markov semigroups will be proven. The talks are almost independent of each other.