Harmonic measure for the mapping class group

Vaibhav Gadre (Harvard)

Abstract: Kaimanovich and Masur showed that a random walk on the mapping class group converges almost surely to a point in the space of projective measured foliations PMF. This defines a harmonic measure on PMF. We shall discuss the relationship of a harmonic measure coming from a finitely supported random walk with the ambient Lebesgue measure class on PMF.