Recurrence of Quadratic Differentials for Harmonic Measure


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.

Cite this paper

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