Central limit theorem in negative curvature
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.
scientific article; zbMATH DE number 823402