CIRM - Videos & books Library - Large stochastic systems of interacting particles

Virtualconference

Auteurs : Jabin, Pierre-Emmanuel (Auteur de la conférence)
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.

Mots-Clés : many-particle systems; large deviation inequalities; singular attractive gradient flow

Codes MSC :
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

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Pierre-Emmanuel_JABIN.pdf

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2021-03-23_Jabin.mp4

Informations sur la Rencontre

Nom de la Rencontre : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse
Organisateurs de la Rencontre : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine
Dates : 22/03/2021 - 26/03/2021
Année de la rencontre : 2021
URL de la Rencontre : https://www.chairejeanmorlet.com/2355.html

Données de citation

DOI : 10.24350/CIRM.V.19734403
Citer cette vidéo: Jabin, Pierre-Emmanuel (2021). Large stochastic systems of interacting particles. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19734403
URI : http://dx.doi.org/10.24350/CIRM.V.19734403

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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, et al. Mean field limit for Coulomb-type flows. Duke Mathematical Journal, 2020, vol. 169, no 15, p. 2887-2935. - http://dx.doi.org/10.1215/00127094-2020-0019

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