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

2022/08/10 by Christophe Andrieu, Andrieu, Christophe, Anthony Lee +5
Mathematics · #60J22 #65C05 #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2208.05239

openalex publication_date 2022/08/10 · openalex created_date 2022/08/12 · openalex updated_date 2026/07/28

Abstract

We develop a theory of weak Poincaré 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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