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Central limit theorem of Brownian motions in pinched negative curvature

Published online by Cambridge University Press:  22 April 2021

JAELIN KIM*
Affiliation:
Department of Mathematical Sciences, Seoul National University, Seoul151-747, Republic of Korea

Abstract

We prove the central limit theorem of random variables induced by distances to Brownian paths and Green functions on the universal cover of Riemannian manifolds of finite volume with pinched negative curvature. We further provide some ergodic properties of Brownian motions and an application of the central limit theorem to the dynamics of geodesic flows in pinched negative curvature.

Type
Original Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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