A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Yuri Bakhtin; Matilde Martánez

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 6, page 1078-1089
  • ISSN: 0246-0203

Abstract

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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 T 1 ℒ of ℒ which is invariant under both the geodesic and the horocycle flows.

How to cite

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Bakhtin, Yuri, and Martánez, Matilde. "A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces." Annales de l'I.H.P. Probabilités et statistiques 44.6 (2008): 1078-1089. <http://eudml.org/doc/78003>.

@article{Bakhtin2008,
abstract = {$\mathcal \{L\}$ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on $\mathcal \{L\}$ is harmonic if and only if it is the projection of a measure on the unit tangent bundle $T^\{1\}\mathcal \{L\}$ of $\mathcal \{L\}$ which is invariant under both the geodesic and the horocycle flows.},
author = {Bakhtin, Yuri, Martánez, Matilde},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {foliated spaces; harmonic measures; brownian motion on the hyperbolic plane; geodesic flow; horocycle flow; Brownian motion on the hyperbolic plane},
language = {eng},
number = {6},
pages = {1078-1089},
publisher = {Gauthier-Villars},
title = {A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces},
url = {http://eudml.org/doc/78003},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Bakhtin, Yuri
AU - Martánez, Matilde
TI - A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 6
SP - 1078
EP - 1089
AB - $\mathcal {L}$ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on $\mathcal {L}$ is harmonic if and only if it is the projection of a measure on the unit tangent bundle $T^{1}\mathcal {L}$ of $\mathcal {L}$ which is invariant under both the geodesic and the horocycle flows.
LA - eng
KW - foliated spaces; harmonic measures; brownian motion on the hyperbolic plane; geodesic flow; horocycle flow; Brownian motion on the hyperbolic plane
UR - http://eudml.org/doc/78003
ER -

References

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