THE POISSON BOUNDARY OF THE MAPPING CLASS GROUPVadim

A theory of random walks on the mapping class group and its non-elementary subgroups is developed. We prove convergence of sample paths in the Thurston compact-iication and show that the space of projective measured foliations with the corresponding harmonic measure can be identiied with the Poisson boundary of random walks. The methods are based on an… (More)