On uniform in time propagation of chaos in the metastable Curie-Weiss model

Pierre LE BRIS
IHES

Date(s) : 13/05/2025 iCal
14h30 - 15h30

Some low temperature particle systems in mean-field interaction are ergodic
with respect to a unique invariant measure,
while their (non-linear) mean-field limit may possess several steady states.
In particular, in such cases, propagation of chaos
(i.e. the convergence of the particle system to its mean-field limit as n,
the number of particles, goes to infinity) cannot hold uniformly in time
since the long-time behaviors of the two processes are a priori incompatible.
However, the particle system may be metastable,
and the time needed to exit the basin of attraction
of one of the steady states of its limit and go to another
is exponentially (in n) long.
Before this exit time,
the particle system reaches a (quasi-)stationary distribution,
which we expect to be a good approximation
of the corresponding non-linear steady state.
The goal of this talk is to study a toy model,
the Curie-Weiss model, and show uniform in time propagation of chaos
of the particle system conditioned to keeping a positive mean.
Based on joint work with L. Journel (Université de Neuchâtel).