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
Journal	International Mathematics Research Notices
DOIs	https://doi.org/10.1093/imrn/rnaa277
Publication status	E-pub ahead of print - 19 Dec 2020

Bibliographical note

rnaa277

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10.1093/imrn/rnaa277

https://doi.org/10.1093/imrn/rnaa277

Cite this

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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.",

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AU - Azemar, Aitor

AU - Gadre, Vaibhav

AU - Jeffreys, Luke

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Y1 - 2020/12/19

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)

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

ER -