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Gadre, Vaibhav S (2009)
Publisher: Duke University Press
Languages: English
Types: Article
Subjects: QA, 20F65, 30F60, 37E30, 32G15, Mathematics - Dynamical Systems, Mathematics - Geometric Topology
Kaimanovich and Masur showed that a random walk on the mapping class group for an initial distribution whose support generates a nonelementary subgroup when projected into Teichm├╝ller space converges almost surely to a point in the space $\mathcal {PMF}$ of projective measured foliations on the surface. This defines a harmonic measure on $\mathcal {PMF}$ . 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 $\mathcal {PMF}$ .
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