15/02/2023, 16:00 — 17:00 — Online
Eric Luçon, Université Paris Cité
How large is the mean-field framework ?
The canonical framework for mean-field systems is to consider $N$ particles (diffusions, or dynamics with jumps, etc) that interact on the complete graph in a uniform way, the strength of interaction between two particles being of size $1/N$. The behavior of the system is hence captured by the empirical measure of the system which converges as $N\to\infty$ to the solution of a nonlinear Fokker Planck equation. The motivation of this talk is simple: what can we say if one no longer interacts on the complete graph, i.e. one removes connections between particles ? if the graph is sufficiently close to the complete graph, one expects the same asymptotic behavior. We will address this question at the level of the LLN and fluctuations of the empirical measure of the system. This is based on joint works with G. Giacomin, S. Delattre, F. Coppini and C. Poquet.
