Displacement convexity of generalized relative entropies. II

Shin Ichi Ohta, Asuka Takatsu

研究成果: Article査読

9 被引用数 (Scopus)

抄録

We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in this class is equivalent to the combination of the non-negative weighted Ricci curvature and the convexity of another weight function used in the definition of the generalized relative entropies. This convexity condition corresponds to Lott and Villani's version of the curvature-dimension condition. As applications, we obtain appropriate variants of the Talagrand, HWI and logarithmic Sobolev inequalities, as well as the concentration of measures. We also investigate the gradient flow of our generalized relative entropy.

本文言語English
ページ(範囲)689-785
ページ数97
ジャーナルCommunications in Analysis and Geometry
21
4
DOI
出版ステータスPublished - 2013
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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