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arXiv · 1605.03874

Dimension of harmonic measures in hyperbolic spaces

Ryokichi Tanaka
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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.

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Ryokichi Tanaka. 2016-05-12. Dimension of harmonic measures in hyperbolic spaces. https://doi.org/10.1017/etds.2017.23

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