Hausdorff spectrum of harmonic measure

Ryokichi Tanaka

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)277-307
Number of pages31
JournalErgodic Theory and Dynamical Systems
Issue number1
Publication statusPublished - 2017 Feb 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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