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Harmonic measures for distributions with finite support on the mapping class group are singular
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Gadre, Vaibhav (2014) Harmonic measures for distributions with finite support on the mapping class group are singular. Duke Mathematical Journal, Volume 163 (Number 2). pp. 309-368. doi:10.1215/00127094-2430368 ISSN 0012-7094.
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Official URL: http://projecteuclid.org/euclid.dmj/1391007589
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Measure algebras, Mappings (Mathematics) | ||||
Journal or Publication Title: | Duke Mathematical Journal | ||||
Publisher: | Duke University Press | ||||
ISSN: | 0012-7094 | ||||
Official Date: | 1 February 2014 | ||||
Dates: |
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Volume: | Volume 163 | ||||
Number: | Number 2 | ||||
Page Range: | pp. 309-368 | ||||
DOI: | 10.1215/00127094-2430368 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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