Poincaré inequalities for Markov chains: a meeting with Cheeger, Lyapunov and Metropolis

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Abstract

We develop a theory of weak Poincar\'e inequalities to characterize convergence rates of ergodic Markov chains. Motivated by the application of Markov chains in the context of algorithms, we develop a relevant set of tools which enable the practical study of convergence rates in the setting of Markov chain Monte Carlo methods, but also well beyond.
Original languageUndefined/Unknown
DOIs
Publication statusPublished - 10 Aug 2022

Bibliographical note

80 pages

Keywords

  • math.PR
  • stat.CO
  • 60J22, 65C05

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