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

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

doi:10.48550/arXiv.2208.05239

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

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

Research output: Working paper › Preprint

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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 language	Undefined/Unknown
DOIs	https://doi.org/10.48550/arXiv.2208.05239
Publication status	Published - 10 Aug 2022

Bibliographical note

80 pages

Keywords

math.PR
stat.CO
60J22, 65C05

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10.48550/arXiv.2208.05239

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Cite this

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