Recurrence of quadratic differentials for harmonic measure

Gadre, V. and Maher, J. (2020) Recurrence of quadratic differentials for harmonic measure. Mathematical Proceedings of the Cambridge Philosophical Society, 169(2), pp. 299-305. (doi: 10.1017/S0305004119000185)

Abstract

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 Teichmüller geodesic is in the principal stratum of quadratic differentials. We show that a Teichmüller geodesic typical with respect to the harmonic measure for such random walks, is recurrent to the thick part of the principal stratum. As a consequence, the vertical foliation of such a random Teichmüller geodesic has no saddle connections.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• 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: Mathematical Proceedings of the Cambridge Philosophical Society
• Publisher: Cambridge University Press
• ISSN: 0305-0041
• ISSN (Online): 1469-8064
• Published Online: 25 June 2019
• Copyright Holders: Copyright © 2019 Cambridge Philosophical Society
• First Published: First published in Mathematical Proceedings of the Cambridge Philosophical Society 169(2): 299-305
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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