Dimension of harmonic measures in hyperbolic spaces
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 spac...
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| Veröffentlicht in: | Ergodic theory and dynamical systems 2019-02, Vol.39 (2), p.474-499 |
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| container_title | Ergodic theory and dynamical systems |
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| creator | TANAKA, RYOKICHI |
| description | 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. |
| doi_str_mv | 10.1017/etds.2017.23 |
| format | Article |
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| ispartof | Ergodic theory and dynamical systems, 2019-02, Vol.39 (2), p.474-499 |
| issn | 0143-3857 1469-4417 |
| language | eng |
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| source | Cambridge Journals |
| subjects | Original Article Random walk Riemann manifold |
| title | Dimension of harmonic measures in hyperbolic spaces |
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