Gadre, V. (2014) Harmonic measures for distributions with finite support on the mapping class group are singular. Duke Mathematical Journal, 163(2), pp. 309-368. (doi: 10.1215/00127094-2430368)
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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 PMFPMF of projective measured foliations on the surface. This defines a harmonic measure on PMFPMF. 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 PMFPMF.
| Item Type: | Articles |
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| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Gadre, Dr Vaibhav |
| Authors: | Gadre, V. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Duke Mathematical Journal |
| Publisher: | Duke University Press |
| ISSN: | 0012-7094 |
| ISSN (Online): | 1547-7398 |
| Copyright Holders: | Copyright © 2014 Duke Mathematical Journal |
| First Published: | First published in Duke Mathematical Journal 163(2):309-368 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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