Harmonic measures for distributions with finite support on the mapping class group are singular

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Harmonic Measures for Distributions with Finite Support on the Mapping Class Group Are Singular

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 ...

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ژورنال

عنوان ژورنال: Duke Mathematical Journal

سال: 2014

ISSN: 0012-7094

DOI: 10.1215/00127094-2430368