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Kaimanovich and Masur showed that a random walk on the mapping class groupfor an initial distribution with finite first moment and whose supportgenerates a non-elementary subgroup, converges almost surely to a point in thespace PMF of projective measured foliations on the surface. This defines aharmonic measure on PMF. Here, we show that when the initial distribution hasfinite support, the corresponding harmonic measure is singular with respect tothe natural Lebesgue measure on PMF.

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