Convergence of non-reversible Markov processes via lifting and flow Poincar{é} inequality
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916850999230464 |
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| author | Eberle, Andreas Guillin, Arnaud Hahn, Leo Lörler, Francis Michel, Manon |
| author_facet | Eberle, Andreas Guillin, Arnaud Hahn, Leo Lörler, Francis Michel, Manon |
| contents | 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{é} inequality, a space-time Poincar{é} 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_04238 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of non-reversible Markov processes via lifting and flow Poincar{é} inequality Eberle, Andreas Guillin, Arnaud Hahn, Leo Lörler, Francis Michel, Manon Analysis of PDEs Functional Analysis Probability 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{é} inequality, a space-time Poincar{é} 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. |
| title | Convergence of non-reversible Markov processes via lifting and flow Poincar{é} inequality |
| topic | Analysis of PDEs Functional Analysis Probability |
| url | https://arxiv.org/abs/2503.04238 |