Exponential decay in the mapping class group

Joseph Maher

doi:10.1112/jlms/jds011

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arXiv · 1104.5543

Exponential decay in the mapping class group

Joseph Maher

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Abstract

We show that the probability that a finitely supported random walk on a non-elementary subgroup of the the mapping class group gives a non-pseudo-Anosov element decays exponentially in the length of the random walk. More generally, we show that if R is a set of mapping class group elements with an upper bound on their translation lengths on the complex of curves, then the probability that a random walk lies in R decays exponentially in the length of the random walk.

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Joseph Maher. 2016-07-06. Exponential decay in the mapping class group. https://doi.org/10.1112/jlms%2Fjds011

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