Central limit theorem in negative curvature
type: Item
instance of: scholarly article
title: Central limit theorem in negative curvature
zbMATH Open document ID: 0839.58064
author: François Ledrappier
published in: The Annals of Probability
publication date: 1996-06-24T00:00:00Z
review text: The author proves a central limit theorem for the distance of the Brownian point on the universal cover \(\widetilde M\) of a compact negatively curved Riemannian manifold \(M\). As the main tool he introduces leafwise Brownian motions on \(\widetilde M\) on the stable foliation associated with the geodesic flow. Then he replaces the processes by semi-Markovian ones driven by the leafwise Brownian motion and shows that there is a contraction in spaces of Hölder continuous functions of sufficiently small exponent. The above result follows from the main result of the paper which is a central limit theorem for leafwise 1-forms evaluated on leafwise Brownian paths when the codifferential of the form is Hölder continuous.
reviewed by: Yuri E. Gliklikh
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 823402
zbMATH Keywords: negative curvature
zbMATH Keywords: central limit theorem
zbMATH Keywords: Brownian motions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988181
OpenAlex ID: W2059299811
DOI: 10.1214/AOP/1176988181
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description: scientific article; zbMATH DE number 823402