Exponential decay in the mapping class group
Geometric Topology
2016-07-07 v3 Group Theory
Probability
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.
Cite
@article{arxiv.1104.5543,
title = {Exponential decay in the mapping class group},
author = {Joseph Maher},
journal= {arXiv preprint arXiv:1104.5543},
year = {2016}
}
Comments
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