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A proof of Harris-type theorems based on semigroup arguments

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FKT - Frontiers in kinetic theory: connecting microscopic to macroscopic scales - KineCon 2022

We will present a recent work in collaboration with Stéphane Mischler in which we prove several probabilistic theorems usually known as “Harris-type” results. These provide rates of convergence to equilibrium for Markov processes, and have been usually proved by coupling arguments in probability. We give simplified proofs using semigroup-type arguments, which include both cases with exponential convergence rates and cases with slower-than-exponential rates. The idea of the proof is a generalisation of arguments by Hairer & Mattingly, and the non-exponential case gives similar results to some obtained by Douc, Fort & Guillin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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