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

Vaibhav S Gadre

doi:10.1215/00127094-2430368

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arXiv · 0911.2891

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

Vaibhav S Gadre

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Abstract

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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BibTeX RIS

Vaibhav S Gadre. 2009-11-15. Harmonic measures for distributions with finite support on the mapping class group are singular. https://doi.org/10.1215/00127094-2430368

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