A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Yuri Bakhtin, Matilde Martínez

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1078-1089
Number of pages12
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume44
Issue number6
DOIs
StatePublished - 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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