Hausdorff spectrum of harmonic measure

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)277-307
ページ数31
ジャーナルErgodic Theory and Dynamical Systems
37
1
DOI
出版ステータスPublished - 2017 2 1

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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