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arXiv · 2208.05239

Poincar\'e inequalities for Markov chains: a meeting with Cheeger, Lyapunov and Metropolis

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

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Christophe Andrieu, Anthony Lee, Sam Power, Andi Q. Wang. 2022-08-10. Poincar\'e inequalities for Markov chains: a meeting with Cheeger, Lyapunov and Metropolis. https://arxiv.org/abs/2208.05239

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