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arXiv · 2503.04238

Convergence of non-reversible Markov processes via lifting and flow Poincar{\'e} inequality

Andreas Eberle·Arnaud Guillin·Leo Hahn·Francis Lörler·Manon Michel
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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 Poincar{\'e} inequality, a space-time Poincar{\'e} 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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Andreas Eberle, Arnaud Guillin, Leo Hahn, Francis Lörler, Manon Michel. 2025-03-06. Convergence of non-reversible Markov processes via lifting and flow Poincar{\'e} inequality. https://arxiv.org/abs/2503.04238

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