A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Yuri Bakhtin; Matilde Martínez

doi:10.1214/07-AIHP147

A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Yuri Bakhtin, Matilde Martínez

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

ℒ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on ℒ is harmonic if and only if it is the projection of a measure on the unit tangent bundle T¹ ℒ of ℒ which is invariant under both the geodesic and the horocycle flows.

Original language	English (US)
Pages (from-to)	1078-1089
Number of pages	12
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	44
Issue number	6
DOIs	https://doi.org/10.1214/07-AIHP147
State	Published - Dec 1 2008

Keywords

Brownian Motion on the hyperbolic plane
Foliated spaces
Geodesic flow
Harmonic measures
Horocycle flow

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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AU - Martínez, Matilde

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AB - ℒ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on ℒ is harmonic if and only if it is the projection of a measure on the unit tangent bundle T1 ℒ of ℒ which is invariant under both the geodesic and the horocycle flows.

KW - Brownian Motion on the hyperbolic plane

KW - Foliated spaces

KW - Geodesic flow

KW - Harmonic measures

KW - Horocycle flow

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A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Abstract

Keywords

ASJC Scopus subject areas

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