Statistical hyperbolicity for harmonic measure

Aitor Azemar; Vaibhav Gadre; Luke Jeffreys

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arXiv · 1909.13811

Statistical hyperbolicity for harmonic measure

Aitor Azemar·Vaibhav Gadre·Luke Jeffreys

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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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Aitor Azemar, Vaibhav Gadre, Luke Jeffreys. 2019-09-30. Statistical hyperbolicity for harmonic measure. https://arxiv.org/abs/1909.13811

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