Modified log-Sobolev inequalities for strongly log-concave distributions

Mary Cryan, Heng Guo, Giorgos Mousa

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the modified log-Sobolev constant for a natural Markov chain which converges to an r-homogeneous strongly log-concave distribution is at least 1/r. Applications include an asymptotically optimal mixing time bound for the bases-exchange walk for matroids, and a concentration bound for Lipschitz functions over these distributions.
Original languageEnglish
Pages (from-to)506-525
Number of pages20
JournalAnnals of Probability
Volume49
Issue number1
DOIs
Publication statusPublished - 22 Jan 2021

Keywords

  • matroids
  • bases exchange walk
  • Markov chains
  • log-Sobolev inequality

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