A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Bakhtin, Yuri; Martánez, Matilde

Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008), p. 1078-1089 / Harvested from Numdam

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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.

Publié le : 2008-01-01

MR 2469335 | Zbl 1189.37033

DOI : https://doi.org/10.1214/07-AIHP147
Classification: 37C12, 58J65, 37D40

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     author = {Bakhtin, Yuri and Mart\'\i nez, Matilde},
     title = {A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {44},
     year = {2008},
     pages = {1078-1089},
     doi = {10.1214/07-AIHP147},
     mrnumber = {2469335},
     zbl = {1189.37033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2008__44_6_1078_0}
}

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) pp. 1078-1089. doi : 10.1214/07-AIHP147. http://gdmltest.u-ga.fr/item/AIHPB_2008__44_6_1078_0/

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