Statistical hyperbolicity for harmonic measure
Aitor Azemar, Vaibhav Gadre, Luke Jeffreys
TL;DR
This paper proves that Teichmuller space exhibits statistical hyperbolicity when considering harmonic measures derived from certain random walks on the mapping class group, highlighting geometric properties of these measures.
Contribution
It establishes the statistical hyperbolicity of Teichmuller space for harmonic measures from random walks with finite first moment and non-elementary support.
Findings
Teichmuller space is statistically hyperbolic under specified harmonic measures.
Harmonic measures considered come from random walks with finite first moment.
Supports generate non-elementary subgroups, ensuring the hyperbolic property.
Abstract
We consider harmonic measures that arise from random walks on the mapping class group determined by probability distributions that have finite first moment with respect to the Teichmuller metric, and whose supports generate non-elementary subgroups. We prove that Teichmuller space with the Teichmuller metric is statistically hyperbolic for such a harmonic measure.
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