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The stratum of random mapping classes

Published online by Cambridge University Press:  02 May 2017

VAIBHAV GADRE  and
JOSEPH MAHER
VAIBHAV GADRE
Affiliation:
School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, UK email Vaibhav.Gadre@glasgow.ac.uk
JOSEPH MAHER
Affiliation:
Department of Mathematics, College of Staten Island, CUNY, 2800 Victory Boulevard, Staten Island, NY 10314, USA email joseph.maher@csi.cuny.edu Department of Mathematics, 4307 Graduate Center, CUNY, 365 5th Avenue, New York, NY 10016, USA
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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. For such random walks, we show that mapping classes along almost every infinite sample path are eventually pseudo-Anosov, with invariant Teichmüller geodesics in the principal stratum. This provides an answer to a question of Kapovich and Pfaff [Internat. J. Algebra Comput.25, 2015 (5) 745–798].

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 7 , October 2018 , pp. 2666 - 2682
Copyright
© Cambridge University Press, 2017 

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