English
The mean-field limit to the Vlasov-Poisson-Fokker-Planck system
Virtualconference
Auteurs : Jabin, Pierre-Emmanuel (Auteur de la Conférence)
CIRM (Editeur )
60F10 - Large deviations
60H30 - Applications of stochastic analysis (to PDE, etc.)
82C22 - Interacting particle systems
35Q70 - PDEs in connection with mechanics of particles and systems
CIRM (Editeur )
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Résumé :
We propose a modulated free energy which combines of the method previously developed by the speaker together with the modulated energy introduced by S. Serfaty. This modulated free energy may be understood as introducing appropriate weights in the relative entropy to cancel the more singular terms involving the divergence of the flow. This modulated free energy allows to treat singular interactions of gradient-flow type and allows potentials with large smooth part, small attractive singular part and large
repulsive singular part. As an example, a full rigorous derivation (with quantitative estimates) of some chemotaxis models, such as Patlak-Keller Segel system in the subcritical regimes, is obtained. This is joint work with D. Bresch and Z. Wang.
Keywords : many-particle systems; large deviation inequalities; singular attractive gradient flows
Codes MSC : repulsive singular part. As an example, a full rigorous derivation (with quantitative estimates) of some chemotaxis models, such as Patlak-Keller Segel system in the subcritical regimes, is obtained. This is joint work with D. Bresch and Z. Wang.
Keywords : many-particle systems; large deviation inequalities; singular attractive gradient flows
60F10 - Large deviations
60H30 - Applications of stochastic analysis (to PDE, etc.)
82C22 - Interacting particle systems
35Q70 - PDEs in connection with mechanics of particles and systems
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 10/05/2022 Date de captation : 25/04/2022 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : PDE ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Durée : 01:03:04 Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2022-04-25_Jabin.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Probability/PDE Interactions: Interface Models and Particle Systems / Interactions EDP/Probabilités : interfaces et systèmes de particulesOrganisateurs de la rencontre : Duerinckx, Mitia ; Gess, Benjamin ; Fathi, Max ; Guillin, Arnaud ; Simon, Marielle Dates : 25/04/2022 - 29/04/2022 Année de la rencontre : 2022 URL Congrès : https://conferences.cirm-math.fr/2557.html
Données de citation
DOI : 10.24350/CIRM.V.19910103Citer cette vidéo: Jabin, Pierre-Emmanuel (2022). The mean-field limit to the Vlasov-Poisson-Fokker-Planck system. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19910103 URI : http://dx.doi.org/10.24350/CIRM.V.19910103 |
Voir aussi
- [Multi angle] Covariance-modulated optimal transport / Auteur de la Conférence Hoffmann, Franca.
- [Multi angle] Einstein's effective viscosity formula / Auteur de la Conférence Gloria, Antoine.
- [Multi angle] Uniqueness of the filtering equations in the space of measures / Auteur de la Conférence Pardoux, Etienne.
- [Multi angle] Disorder relevance for non-convex random gradient Gibbs measures in d ≤ 2 / Auteur de la Conférence Cotar, Codina.
Bibliographie
- BRESCH, Didier, JABIN, Pierre-Emmanuel, et WANG, Zhenfu. On mean-field limits and quantitative estimates with a large class of singular kernels: application to the Patlak–Keller–Segel model. Comptes Rendus Mathematique, 2019, vol. 357, no 9, p. 708-720. - https://doi.org/10.1016/j.crma.2019.09.007
- JABIN, Pierre-Emmanuel et WANG, Zhenfu. Quantitative estimates of propagation of chaos for stochastic systems with $W^{-1,\infty}$ kernels. Inventiones mathematicae, 2018, vol. 214, no 1, p. 523-591. - https://doi.org/10.1007/s00222-018-0808-y
- SERFATY, Sylvia. Mean field limit for Coulomb-type flows. Duke Mathematical Journal, 2020, vol. 169, no 15, p. 2887-2935. - https://doi.org/10.1215/00127094-2020-0019
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