## Stable Strata of Geodesics in Outer Space (2017)

- Yael Algom-Kfir, Ilya Kapovich, Catherine Pfaff
- 2017

- Published 2017

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 of quadratic differentials. We show that a Teichmüller geodesic typical with respect to the harmonic measure for such random walks, is recurrent to the thick part of the principal stratum. As a consequence, the vertical foliation of such a random Teichmüller geodesic has no saddle connections.

@inproceedings{GADRE2017RecurrenceOQ,
title={Recurrence of Quadratic Differentials for Harmonic Measure},
author={VAIBHAV GADRE and Joseph Maher},
year={2017}
}