$\mathcal{L}$ 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.
Publié le : 2008-12-15
Classification:
Foliated spaces,
harmonic measures,
Brownian Motion on the hyperbolic plane,
geodesic flow,
horocycle flow,
37C12,
58J65,
37D40
@article{1227287565,
author = {Bakhtin, Yuri and Mart\'\i nez, Matilde},
title = {A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 1078-1089},
language = {en},
url = {http://dml.mathdoc.fr/item/1227287565}
}
Bakhtin, Yuri; Martínez, Matilde. A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 1078-1089. http://gdmltest.u-ga.fr/item/1227287565/