Harmonic Measures for Distributions with Finite Support on the Mapping Class Group Are Singular
نویسنده
چکیده
Kaimanovich and Masur [14] showed that a random walk on the mapping class group for an initial distribution whose support generates a non-elementary subgroup, when projected into Teichmüller space converges almost surely to a point in the space P M F of projective measured foliations on the surface. This defines a harmonic measure on P M F . Here, we show that when the initial distribution has finite support, the corresponding harmonic measure is singular with respect to the natural Lebesgue measure class on P M F .
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