Weakly Interacting Particle system: a crash course

schedule le lundi 17 décembre 2018 de 17h00 à 18h00

Organisé par : G. Conchon--Kerjan, B. Dembin

Intervenant : Fabio Coppini (LPSM)
Lieu : Salle 1016, Bâtiment Sophie Germain, Paris 7 Diderot

Sujet : Weakly Interacting Particle system: a crash course

Résumé :

This exposé will focus on a rather big class of interacting particle models: a bunch of particles which satisfy a system of coupled (stochastic) differential equations, the coupling from one equation to another being weak in a sense to be precised. Mathematical results for such systems as LLN, Propagation of chaos and Large Deviations have been seriously addressed between the 80's and the 90's, but many questions, as the long time behavior for a finite system, have remained unsolved. These questions, together with the new ones coming from mean-field games and McKean-Vlasov limits in finance, constitute a big part of current research. I will try to recall the history, the results and the main reasons why these models were introduced and why they are still important.