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Statut |
Confirmé |
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Série |
SEED |
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Domaines |
math-ph |
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Date |
Mercredi 9 Juillet 2025 |
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Heure |
10:30 |
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Institut |
IHES |
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Salle |
Amphithéâtre Léon Motchane |
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Nom de l'orateur |
Eichinger |
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Prenom de l'orateur |
Katharina |
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Addresse email de l'orateur |
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Institution de l'orateur |
LMO, Paris-Saclay and Inria ParMA, Orsay |
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Titre |
Lipschitz continuity of diffusion transport maps from a control perspective |
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Résumé |
Lipschitz transport maps between two measures are useful tools for transferring
analytical properties, such as functional inequalities. The most well-known result
in this field is Caffarelli’s contraction theorem, which shows that the optimal
transport map from a Gaussian to a uniformly log-concave measure is globally
Lipschitz. Note that the transfer of analytical properties does not depend on the
optimality of the transport map. This is why several works have established
Lipschitz bounds for other transport maps, such as those derived from diffusion
processes, as introduced by Kim and Milman. Here, we use the control
interpretation of the transport vector field inducing the transport map and a
coupling strategy to obtain Lipschitz bounds for this map between asymptotically
log-concave measures and their Lipschitz perturbations. This talk is based on a
joint work with Giovanni Conforti. |
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Numéro de preprint arXiv |
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Commentaires |
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Fichiers attachés |
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