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The mean-field limit to the Vlasov-Poisson-Fokker-Planck system
Virtualconference
Authors : Jabin, Pierre-Emmanuel (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 10/05/2022 Conference Date : 25/04/2022 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : PDE ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 01:03:04 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2022-04-25_Jabin.mp4 
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Information on the Event
Event Title : Probability/PDE Interactions: Interface Models and Particle Systems / Interactions EDP/Probabilités : interfaces et systèmes de particulesEvent Organizers : Duerinckx, Mitia ; Gess, Benjamin ; Fathi, Max ; Guillin, Arnaud ; Simon, Marielle Dates : 25/04/2022 - 29/04/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2557.html
Citation Data
DOI : 10.24350/CIRM.V.19910103Cite this video as: 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 |
See Also
- [Multi angle] Covariance-modulated optimal transport / Author of the conference Hoffmann, Franca.
- [Multi angle] Einstein's effective viscosity formula / Author of the conference Gloria, Antoine.
- [Multi angle] Uniqueness of the filtering equations in the space of measures / Author of the conference Pardoux, Etienne.
- [Multi angle] Disorder relevance for non-convex random gradient Gibbs measures in d ≤ 2 / Author of the conference Cotar, Codina.
Bibliography
- 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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