PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws / Interactions EDP/Probabilités : systèmes de particules, lois de conservation hyperboliques

Collection PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws / Interactions EDP/Probabilités : systèmes de particules, lois de conservation hyperboliques

Several fundamental equations from physics describe systems composed of a large number N of interacting particles. These equations play a role in a wide number of fields, such as kinetic theory of gases and plasmas, chemotaxy, po- pulation dynamics, etc. Rigorously justifying the convergence of microscopic models describing the evolution of the N particles to mesoscopic or macroscopic nonlinear models in a restricted phase space is a major goal in applied mathema- tics. The interactions inside the system may be modelled by either deterministic or stochastic dynamics. This conference, on the interplay between PDEs and probability, and following a previous edition that took place at the CIRM in 2017, will focus on the study of such particle systems, with an emphasis on mean-fields models with singular interactions, such as the Boltzman, Landau and Keller-Segel equations, as well as systems of conservation laws, which arise as scaling limits of asymmetric particle systems under hyperbolic scaling. Our aim is to foster contacts between specialists of the varied areas of probability and PDEs that are connected to these topics, in order to develop new methods and applications.


Organizer(s) Caputo, Pietro ; Fathi, Max ; Guillin, Arnaud ; Reygner, Julien
Date(s) 14/10/2019 - 18/10/2019
linked URL https://conferences.cirm-math.fr/2083.html
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