Convergence of non-reversible Markov processes via lifting and flow Poincaré inequality

2025/03/06 by Andreas Eberle, Arnaud Guillin, Eberle, Andreas +7 · 7 citations
Mathematics · #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2503.04238

Abstract

We propose a general approach for quantitative convergence analysis of non-reversible Markov processes, based on the concept of second-order lifts and a variational approach to hypocoercivity. To this end, we introduce the flow Poincaré inequality, a space-time Poincaré inequality along trajectories of the semigroup, and a general divergence lemma based only on the Dirichlet form of an underlying reversible diffusion. We demonstrate the versatility of our approach by applying it to a pair of run-and-tumble particles with jamming, a model from non-equilibrium statistical mechanics, and several piecewise deterministic Markov processes used in sampling applications, in particular including general stochastic jump kernels.

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