We consider harmonic measures that arise from random walks on the mapping class group determined by probability distributions that have finite first moments with respect to the Teichmüller metric and whose supports generate nonelementary subgroups. We prove that Teichmüller space with the Teichmüller metric is statistically hyperbolic for such a harmonic measure.
|Journal||International Mathematics Research Notices|
|Early online date||19 Dec 2020|
|Publication status||Published - Apr 2022|