Dimension of harmonic measures in hyperbolic spaces
Probability
2019-02-20 v3 Dynamical Systems
Group Theory
Abstract
We show exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under 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.
Keywords
Cite
@article{arxiv.1605.03874,
title = {Dimension of harmonic measures in hyperbolic spaces},
author = {Ryokichi Tanaka},
journal= {arXiv preprint arXiv:1605.03874},
year = {2019}
}
Comments
Final version, to appear in Ergodic Theory and Dynamical Systems