Statistical Hyperbolicity for Harmonic Measure

Aitor Azemar; Vaibhav Gadre; Luke Jeffreys

doi:10.1093/imrn/rnaa277

Statistical Hyperbolicity for Harmonic Measure

Aitor Azemar
, Vaibhav Gadre^*
, Luke Jeffreys

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

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.

Original language	English
Pages (from-to)	6289–6309
Journal	International Mathematics Research Notices
Volume	2022
Issue number	8
Early online date	19 Dec 2020
DOIs	https://doi.org/10.1093/imrn/rnaa277
Publication status	Published - Apr 2022

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rnaa277

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https://arxiv.org/abs/1909.13811

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title = "Statistical Hyperbolicity for Harmonic Measure",

abstract = "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 Teichm{\"u}ller metric and whose supports generate nonelementary subgroups. We prove that Teichm{\"u}ller space with the Teichm{\"u}ller metric is statistically hyperbolic for such a harmonic measure.",

author = "Aitor Azemar and Vaibhav Gadre and Luke Jeffreys",

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AU - Gadre, Vaibhav

AU - Jeffreys, Luke

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N2 - 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.

AB - 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.

U2 - 10.1093/imrn/rnaa277

DO - 10.1093/imrn/rnaa277

M3 - Article (Academic Journal)

SN - 1073-7928

VL - 2022

SP - 6289

EP - 6309

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 8

ER -

Statistical Hyperbolicity for Harmonic Measure

Abstract

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