A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Bakhtin, Yuri; Martánez, Matilde

doi:10.1214/07-AIHP147

Bakhtin, Yuri ; Martánez, Matilde

Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 6, pp. 1078-1089.

Résumé
Abstract

$ℒ$ denote une lamination (compacte, nonsingulière) par surfaces de Riemann hyperboliques. On montre qu’ une mesure sur $ℒ$ est harmonique si et seulement si elle est la projection d’une mesure sur le fibré tangent unitaire $T^{1} ℒ$ qui est invariante sous les flots géodesique et horocyclique.

$ℒ$ 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.

MR Zbl | 1 citation dans Numdam

DOI : 10.1214/07-AIHP147

Classification : 37C12, 58J65, 37D40
Mots-clés : foliated spaces, harmonic measures, brownian motion on the hyperbolic plane, geodesic flow, horocycle flow

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     author = {Bakhtin, Yuri and Mart\'anez, Matilde},
     title = {A characterization of harmonic measures on laminations by hyperbolic {Riemann} surfaces},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1078--1089},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {6},
     year = {2008},
     doi = {10.1214/07-AIHP147},
     mrnumber = {2469335},
     zbl = {1189.37033},
     language = {en},
     url = {https://www.numdam.org/articles/10.1214/07-AIHP147/}
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Bakhtin, Yuri; Martánez, Matilde. A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 6, pp. 1078-1089. doi : 10.1214/07-AIHP147. https://www.numdam.org/articles/10.1214/07-AIHP147/

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