The Poisson Boundary of Teichm Uller Space
نویسندگان
چکیده
For a Markov operator on Teichm uller space commuting with the action of the mapping class group we prove convergence of sample paths of the associated Markov chain in the Thurston compactiication and show that the Poisson boundary of the Markov operator can be identiied with the space of projective measured foliations. The approach consists in using the authors' results on the Poisson boundary of the mapping class group in combination with a discretization procedure based on a Harnack inequality for Markov operators on Teichm uller space.
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The Poisson Boundary of the Mapping Class Group
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