2016/05/31 by Ryokichi Tanaka
Computer Science · Mathematics · #Brownian motion #Curse of dimensionality #Dimension (graph theory) #Entropy (arrow of time) #Fractal #Fractal dimension #Geometric Analysis and Curvature Flows #Harmonic #Hausdorff dimension #Hyperbolic function #Hyperbolic manifold #Hyperbolic space #Manifold (fluid mechanics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Minkowski–Bouligand dimension #Packing dimension #Physics #Pure mathematics #Random walk #Relatively hyperbolic group #Riemannian manifold #Space (punctuation) #Statistics #Topological and Geometric Data Analysis #math.DS #math.GR #math.PR
paper · pdf · doi:10.1017/etds.2017.23
published as Ergod. Th. Dynam. Sys. 39 (2019) 474-499 · Final version, to appear in Ergodic Theory and Dynamical Systems
arxiv created 2017/02/11 · openalex publication_date 2017/05/02 · arxiv updated 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.