The stratum of random mapping classes

Vaibhav Gadre; Joseph Maher

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arXiv · 1607.01281

The stratum of random mapping classes

Vaibhav Gadre·Joseph Maher

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Abstract

We consider random walks on the mapping class group whose support generates a non-elementary subgroup and contains a pseudo-Anosov map whose invariant Teichm\"uller 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 Teichm\"uller geodesics in the principal stratum. This provides an answer to a question of Kapovich and Pfaff.

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Vaibhav Gadre, Joseph Maher. 2016-07-05. The stratum of random mapping classes. https://arxiv.org/abs/1607.01281

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