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

Let Gamma be a geometrically finite Kleinian group, relative to the hyperbo lic space H = Hd+1 and let delta denote the Hausdorff dimension of its limi t set, that we suppose here strictly larger than d/2. We prove a central li mit theorem for the geodesic flow on the manifold M := Gamma \H, with respe ct to the Patterson-Sullivan measure. The argument uses the ground-state di ffusion and its canonical lift to the frame bundle, for which the existence of a potential operator is proved. (C) 2001 Editions scientifiques et medi cales Elsevier SAS.