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Contractive coupling rates and curvature lower bounds for reversible Markov chains| title | Contractive coupling rates and curvature lower bounds for reversible Markov chains |
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| start_date | 2024/12/11 |
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| schedule | 14h15 |
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| online | no |
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| location_info | salle Sophie Germain 1013 |
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| summary | Ricci curvature lower bounds for Riemannian manifolds have been linked to many functional inequalities: this has motivated the seminal independent works of Sturm and Lott and Villani, who extended the notion of curvature lower bound and many of its consequences to a large class of metric measure spaces. In spite of its generality, this theory does not apply to Markov chains on discrete spaces; for this reason, several adapted notions of curvature have been proposed, based on different equivalent characterizations of curvature of Riemannian manifolds. Different notions have different pros and cons: e.g., the entropic curvature of Erbar and Maas is hard to compute in some examples, while Ollivier’s coarse Ricci curvature does not imply a modified logarithmic Sobolev inequality. In the present work, adapting arguments of a recent article by Conforti, we show how contractive coupling rates (a concept naturally connected to Ollivier’s curvature) can be used to establish entropic curvature lower bounds for some examples of reversible Markov chains. |
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| responsibles | Vernier, Merle |
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Workflow history| from state (1) | to state | comment | date |
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| submitted | published | | 2024/12/04 14:28 UTC |
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