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Large stochastic systems of interacting particles
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
Additional resources :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Pierre-Emmanuel_JABIN.pdf
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 flow
MSC Codes : Keywords : many-particle systems; large deviation inequalities; singular attractive gradient flow
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
Additional resources :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Pierre-Emmanuel_JABIN.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 09/04/2021 Conference Date : 23/03/2021 Subseries : Research talks arXiv category : Analysis of PDEs ; Mathematical Physics Mathematical Area(s) : PDE ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:35:54 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-23_Jabin.mp4 
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Information on the Event
Event Title : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et AnalyseEvent Organizers : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine Dates : 22/03/2021 - 26/03/2021 Event Year : 2021 Event URL : https://www.chairejeanmorlet.com/2355.html
Citation Data
DOI : 10.24350/CIRM.V.19734403Cite this video as: 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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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, 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
