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1 February 2014 Harmonic measures for distributions with finite support on the mapping class group are singular
Vaibhav Gadre
Duke Math. J. 163(2): 309-368 (1 February 2014). DOI: 10.1215/00127094-2430368

Abstract

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 Teichmüller space 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 class on PMF.

Citation

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Vaibhav Gadre. "Harmonic measures for distributions with finite support on the mapping class group are singular." Duke Math. J. 163 (2) 309 - 368, 1 February 2014. https://doi.org/10.1215/00127094-2430368

Information

Published: 1 February 2014
First available in Project Euclid: 29 January 2014

zbMATH: 1285.30025
MathSciNet: MR3161316
Digital Object Identifier: 10.1215/00127094-2430368

Subjects:
Primary: 30F60, 32G15

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 2 • 1 February 2014
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