Complete Logarithmic Sobolev inequality via Ricci curvature bounded below II

Michael Brannan, Li Gao, Marius Junge

Research output: Contribution to journalArticlepeer-review


We study the "geometric Ricci curvature lower bound", introduced previously by Junge, Li and LaRacuente, for a variety of examples including group von Neumann algebras, free orthogonal quantum groups ON+, q-deformed Gaussian algebras and quantum tori. In particular, we show that Laplace operator on ON+ admits a factorization through the Laplace-Beltrami operator on the classical orthogonal group, which establishes the first connection between these two operators. Based on a non-negative curvature condition, we obtain the completely bounded version of the modified log-Sobolev inequalities for the corresponding quantum Markov semigroups on the examples mentioned above. We also prove that the "geometric Ricci curvature lower bound"is stable under tensor products and amalgamated free products. As an application, we obtain a sharp Ricci curvature lower bound for word-length semigroups on free group factors.

Original languageEnglish (US)
Pages (from-to)741-794
Number of pages54
JournalJournal of Topology and Analysis
Issue number3
StatePublished - Sep 1 2023


  • Quantum Markov semigroup
  • Ricci curvature
  • group von Neumann algebra
  • modified logarithmic Sobolev inequality
  • quantum group

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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