Central Limit Theorem for Leafwise Brownian Motions on Mapping Tori

Abstract

We consider the leafwise Brownian motion on a mapping torus of a homeomorphism on a compact metric space. We prove a central limit theorem for a class of additive functionals of the leafwise Brownian motion starting at any quasi-regular point and apply it to the leafwise Brownian motions on generalized Kronecker foliations. As an auxiliary result, we also give an elementary proof of the characterization of harmonic measures for the leafwise Brownian motion on the mapping torus.