Dimension of harmonic measures in hyperbolic spaces

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.

arXiv commentFinal version, to appear in Ergodic Theory and Dynamical Systems

References in corpus (5)

• On self-similar sets with overlaps and inverse theorems for entropy
• Ledrappier-Young formula and exact dimensionality of self-affine measures
• Analyticity of the entropy and the escape rate of random walks in hyperbolic groups
• Hausdorff spectrum of harmonic measure
• Regularity of the drift and entropy of random walks on groups

Cited by in corpus (4)

• Entropy and drift for word metric on relatively hyperbolic groups
• Random walk speed is a proper function on Teichmüller space
• Limit distributions of branching Markov chains
• Large deviations and rate of escape for hyperbolic random walks