Local convergence for mean-field particle approximation of Wasserstein gradient flow

par Pierre Monmarché (Université Gustave Eiffel)

mardi 14 avr. 2026, 09:50 → 10:50 Europe/Paris

Salle K. Johnson (1R3-1er étage)

Wasserstein gradient flows of free energies are non-linear PDE which can be interpreted in terms of McKean-Vlasov self-interacting diffusion processes. In practice, using propagation of chaos, they are approximated by systems of mean-field interacting particles. Up to now, most works have studied the long-time convergence of these flows and the associated particles in the relatively simple situation where the free energy has a unique critical point which is  the global minimizer, and the invariant Gibbs measure of the N-particle system satisfies a log-Sobolev inequality independent from N. In this talk we focus on the other situation, which occurs for the case for the Curie-Weiss model in a multi-well potential at low temperature. In that case, the particle system is metastable and propagation of chaos cannot hold uniformly in time. We will see how it is still possible to get local convergence estimates of practical interest, which describe a fast convergence (i.e. at a rate independent from N) toward a local minimizer and uniform propagation of chaos for a time scale  exponentially large with N.