CS05: Recent advances in interacting Brownian particle systems and their mean-field limits

date: 7/17/2025, time: 14:00-15:30, room: ICS 13

Organizer: Armand Bernou (Université Claude Bernard Lyon 1)

Chair: Armand Bernou (Université Claude Bernard Lyon 1)

Supervised classification for interacting particle systems


Yating Liu (Paris-Dauphine University)

In this talk, we present a supervised classification method for K distinct interacting particle systems, each characterized by a different drift coefficient function, within the framework of the McKean-Vlasov equation. In these systems, particles are identically distributed but not independent. The central question we address is: given discrete observations of a new particle, how can we determine to which system it belongs? Our approach uses a plug-in classification rule based on estimated drift functions, also relies on the propagation of chaos property. This is joint work with Christophe Denis and Charlotte Dion-Blanc.

Bibliography

\([1]\) Denis, C., Dion-Blanc, C., Liu, Y. (2025) Supervised classification for interacting particle systems, in progress.

Quasi-continuity method for mean-field systems : fluctuations and large deviations

Louis-Pierre Chaintron (École Normale Supérieure de Paris (ENS))

Interacting particle systems have numerous applications in statistical physics, biological modeling, optimization algorithms, and filtering, among others. For systems exhibiting a mean-field structure, the scaling limit is commonly referred to as the "propagation of chaos," a concept introduced in the foundational works of Boltzmann. For such systems with regular coefficients, I will present a particularly simple method for computing the limit. This method, originating from Tanaka (1984), offers an intuitive way to represent high-dimensional systems by drawing an analogy to ordinary differential equations (ODEs), focusing on characteristic curves rather than the underlying partial differential equations (PDEs). In the case of systems with additive noise, the computation of fluctuations and large deviations follows straightforwardly. By using an appropriate discretization, I will also demonstrate how these results can be extended to systems with multiplicative noise and more general types of interactions.

Control of correlation functions in mean-field systems and consequences

Armand BERNOU (Université Claude Bernard Lyon 1)

This talk will focus on mean-field particle systems with small, non-singular interactions and some noise. For such systems, ergodic properties of the mean-field limit PDE typically yield a uniform-in-time propagation of chaos property, which provides a first-order description of the system as \(N\) goes to infinity. I will discuss recent results allowing to derive higher-order description of the system through a uniform-in-time control of many-body correlation functions. Some consequences on the phenomena of creation of chaos and Gibbs relaxation will also be mentioned. Based on joint works with Mitia Duerinckx and Matthieu Ménard.