The stratum of random mapping classes

Gadre, V. and Maher, J. (2018) The stratum of random mapping classes. Ergodic Theory and Dynamical Systems, 38(7), pp. 2666-2682. (doi: 10.1017/etds.2016.132)

131384.pdf - Accepted Version



We consider random walks on the mapping class group that have finite first moment with respect to the word metric, whose support generates a non-elementary subgroup and contains a pseudo-Anosov map whose invariant Teichmuller geodesic is in the principal stratum. For such random walks, we show that mapping classes along almost every infinite sample path are eventually pseudo-Anosov, with invariant Teichmuller geodesics in the principal stratum. This provides an answer to a question of Kapovich-Pfaff.

Item Type:Articles
Additional Information:The first author acknowledges support from the GEAR Network (U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 ‘RNMS: GEometric structures And Representation varieties’). The second author acknowledges support from the Simons Foundation and PSC-CUNY.
Glasgow Author(s) Enlighten ID:Gadre, Dr Vaibhav
Authors: Gadre, V., and Maher, J.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Ergodic Theory and Dynamical Systems
Publisher:Cambridge University Press
ISSN (Online):1469-4417
Published Online:02 May 2017
Copyright Holders:Copyright © 2017 Cambridge University Press
First Published:First published in Ergodic Theory and Dynamical Systems 38(7):2666-2682
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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