Exponential decay in the mapping class group

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.

24 pages, 8 figures. v2: Fixed abstract. v3: Anna Lenzhen pointed out an error in the proof of Lemma 2.11, fixed in this version

References in corpus (1)

• Sieve methods in group theory II: The Mapping Class Group

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