Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Central limit theorem for the geodesic flow associated with a Kleinian group, case delta > d/2


Code(s) de Classification MSC:

Résumé: Let $\,\G\, $ be a geometrically finite Kleinian group, relative to the hyperbolic space $\,\H =\H^{d+1}\, $, and let $\,\d\, $ denote the Hausdorff dimension of its limit set, that we suppose here strictly larger than $\, d/2\, $. We prove a central limit theorem for the geodesic flow on the manifold $\,\M := \G\sm\H\, $, with respect to the Patterson-Sullivan measure. The argument uses the ground-state diffusion and its canonical lift to the frame bundle, for which the existence of a potential operator is proved.

Mots Clés: geodesic flow ; hyperbolic manifold of infinite volume ; diffusion process ; stable foliation ; spectral gap ; Patterson-Sullivan measure ; central limit theorem

Date: 2000-07-10

Prépublication numéro: PMA-603