TY - JOUR
T1 - Hausdorff spectrum of harmonic measure
AU - Tanaka, Ryokichi
N1 - Publisher Copyright:
© Cambridge University Press, 2015A.
PY - 2017/2/1
Y1 - 2017/2/1
N2 - For every non-elementary hyperbolic group, we show that for every random walk with finitely supported admissible step distribution, the associated entropy equals the drift times the logarithmic volume growth if and only if the corresponding harmonic measure is comparable with Hausdorff measure on the boundary. Moreover, we introduce one parameter family of probability measures which interpolates a Patterson-Sullivan measure and the harmonic measure, and establish a formula of Hausdorff spectrum (multifractal spectrum) of the harmonic measure. We also give some finitary versions of dimensional properties of the harmonic measure.
AB - For every non-elementary hyperbolic group, we show that for every random walk with finitely supported admissible step distribution, the associated entropy equals the drift times the logarithmic volume growth if and only if the corresponding harmonic measure is comparable with Hausdorff measure on the boundary. Moreover, we introduce one parameter family of probability measures which interpolates a Patterson-Sullivan measure and the harmonic measure, and establish a formula of Hausdorff spectrum (multifractal spectrum) of the harmonic measure. We also give some finitary versions of dimensional properties of the harmonic measure.
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U2 - 10.1017/etds.2015.48
DO - 10.1017/etds.2015.48
M3 - Article
AN - SCOPUS:84937604139
SN - 0143-3857
VL - 37
SP - 277
EP - 307
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 1
ER -