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

Article, Preprint, Other literature type English OPEN
Gadre, Vaibhav (2014)

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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