Dimension of harmonic measures in hyperbolic spaces

Ryokichi Tanaka

4 被引用数 (Scopus)

抄録

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.

本文言語 English 474-499 26 Ergodic Theory and Dynamical Systems 39 2 https://doi.org/10.1017/etds.2017.23 Published - 2019 2月 1

• 数学 (全般)
• 応用数学

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