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Central limit theorem of Brownian motions in pinched negative curvature

Part of: Dynamical systems with hyperbolic behavior Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  22 April 2021

JAELIN KIM Open the ORCID record for JAELIN KIM [Opens in a new window]
JAELIN KIM*
Affiliation:
Department of Mathematical Sciences, Seoul National University, Seoul151-747, Republic of Korea
*
e-mail: kimjl@snu.ac.kr
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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.

Keywords

foliated Brownian motioncentral limit theoremgeodesic flow in negative curvature

MSC classification

Primary: 58J65: Diffusion processes and stochastic analysis on manifolds
Secondary: 37D35: Thermodynamic formalism, variational principles, equilibrium states 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 7 , July 2022 , pp. 2352 - 2381
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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