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

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

2009-11-15

arxiv.org/abs/0911.2891v2

Mathematics

Geometric Topology

43 pages, 16 figures. Minor improvements overall, specifically Section 12. Added references

Scientific paper

Kaimanovich and Masur showed that a random walk on the mapping class group for an initial distribution with finite first moment and whose support generates a non-elementary subgroup, converges almost surely to a point in the space PMF of projective measured foliations on the surface. This defines a harmonic measure on 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 on PMF.

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