Dimension-free log-Sobolev inequalities for mixture distributions

Hong Bin Chen, Sinho Chewi, Jonathan Niles-Weed

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that if (Px)x∈X is a family of probability measures which satisfy the log-Sobolev inequality and whose pairwise chi-squared divergences are uniformly bounded, and μ is any mixing distribution on X, then the mixture ∫Pxdμ(x) satisfies a log-Sobolev inequality. In various settings of interest, the resulting log-Sobolev constant is dimension-free. In particular, our result implies a conjecture of Zimmermann and Bardet et al. that Gaussian convolutions of measures with bounded support enjoy dimension-free log-Sobolev inequalities.

Original languageEnglish (US)
Article number109236
JournalJournal of Functional Analysis
Volume281
Issue number11
DOIs
StatePublished - Dec 1 2021

Keywords

  • Dimension-free
  • Log-Sobolev inequality
  • Mixture distribution

ASJC Scopus subject areas

  • Analysis

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