TY - JOUR
T1 - Dimension of harmonic measures in hyperbolic spaces
AU - Tanaka, Ryokichi
N1 - Funding Information:
The author would like to thank Pierre Mathieu for a discussion from which this work arose, leading to subsequent discussions with him, Vadim A. Kaimanovich for helpful (and also stimulating) discussions and useful suggestions, Francois Ledrappier for comments on the historical background, Takefumi Kondo for useful discussions, Sebastien Alvarez, Behrang Forghani and Yuval Peres for helpful feedback, and anonymous referees for reading the manuscript carefully and for helpful comments. The author is supported by JSPS Grant-in-Aid for Young Scientists (B) 26800029.
Publisher Copyright:
© 2017 Cambridge University Press.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
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U2 - 10.1017/etds.2017.23
DO - 10.1017/etds.2017.23
M3 - Article
AN - SCOPUS:85018429295
VL - 39
SP - 474
EP - 499
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 2
ER -