Large stochastic systems of interacting particles

Abstract: I will present some recent results, obtained with D. Bresch and Z. Wang, on large stochastic many-particle or multi-agent systems. Because such systems are conceptually simple but exhibit a wide range of emerging macroscopic behaviors, they are now employed in a large variety of applications from Physics (plasmas, galaxy formation...) to the Biosciences, Economy, Social Sciences.

The number of agents or particles is typically quite large, with 1020-1025 particles in many Physics settings for example and just as many equations. Analytical or numerical studies of such systems are potentially very complex leading to the key question as to whether it is possible to reduce this complexity, notably thanks to the notion of propagation of chaos (agents remaining almost uncorrelated).

To derive this propagation of chaos, we have introduced a novel analytical method, which led to the resolution of two long-standing conjectures:

- The quantitative derivation of the 2-dimensional incompressible Navier-Stokes system from the point vortices dynamics;

- The derivation of the mean-field limit for attractive singular interactions such as in the Keller-Segel model for chemotaxis and some Coulomb gases.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysis

Audience: researchers in the topic

"Partial Differential Equations and Applications" Webinar