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

Christophe Andrieu, Anthony Lee, Sam Power, Andi Q. Wang

Published 2022-08-10Version 1

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.