Ricci curvature bounds for weakly interacting Markov chains

Matthias Erbar, Christopher Henderson, Georg Menz, Prasad Tetali

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain curvature bounds in several examples, namely: Glauber dynamics for a class of spin systems including the Ising and Curie-Weiss models, a class of hard-core models and random walks on groups induced by a conjugacy invariant set of generators.

Original languageEnglish (US)
Article number40
JournalElectronic Journal of Probability
Volume22
DOIs
StatePublished - 2017
Externally publishedYes

Keywords

  • Cayley graph
  • Hardcore model
  • Ising model
  • Markov chain
  • Modified logarithmic Sobolev inequality
  • Random walk
  • Ricci curvature

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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