no. 6
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.

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.

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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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. http://www.numdam.org/articles/10.1214/07-AIHP147/

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