Dimension of harmonic measures in hyperbolic spaces

Ryokichi Tanaka

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)474-499
Number of pages26
JournalErgodic Theory and Dynamical Systems
Issue number2
Publication statusPublished - 2019 Feb 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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