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

N. Enriquez, J. Franchi, Y. Le Jan

Research output: Contribution to journalArticlepeer-review

Abstract

Let Γ be a geometrically finite Kleinian group, relative to the hyperbolic space ℍ = ℍd+1, and let δ 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 := Γ\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.

Original languageEnglish (US)
Pages (from-to)153-175
Number of pages23
JournalJournal des Mathematiques Pures et Appliquees
Volume80
Issue number2
DOIs
StatePublished - Mar 2001

Keywords

  • Central limit theorem
  • Diffusion process
  • Geodesic flow
  • Hyperbolic manifold of infinite volume
  • Patterson-Sullivan measure
  • Spectral gap
  • Stable foliation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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