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Dimension of harmonic measures in hyperbolic spaces

Published online by Cambridge University Press:  02 May 2017

RYOKICHI TANAKA
RYOKICHI TANAKA*
Affiliation:
Mathematical Institute, Tohoku University, 6-3 Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan email rtanaka@m.tohoku.ac.jp
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Abstract

We show the exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under a finite first moment condition, and establish the dimension formula by the entropy over the drift. We also treat the case when a group acts on a non-proper hyperbolic space acylindrically. Applications of this formula include continuity of the Hausdorff dimension with respect to driving measures and Brownian motions on regular coverings of a finite volume Riemannian manifold.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 2 , February 2019 , pp. 474 - 499
Copyright
© Cambridge University Press, 2017 

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