The Poisson boundary of the mapping class group

@article{Kaimanovich1994ThePB,
  title={The Poisson boundary of the mapping class group},
  author={Vadim A. Kaimanovich and Howard A. Masur},
  journal={Inventiones mathematicae},
  year={1994},
  volume={125},
  pages={221-264}
}
Abstract. 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 compactification and show that the space of projective measured foliations with the corresponding harmonic measure can be identified with the Poisson boundary of random walks. The methods are based on an analysis of the asymptotic geometry of Teichmüller space and of the contraction properties of the action of the mapping class group… 

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