Long-time propagation of chaos and exit times for metastable mean-field particle systems
Abstract
Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field deterministic limit has several stationary solutions, and the empirical measure of the particle system is then expected to be a metastable process in the space of probability measures, exhibiting rare transitions between the vicinity of these stationary solutions. We show two results in this direction: first, the exit time from such metastable domains occurs at time exponentially large with the number of particles and follows approximately an exponential distribution; second, up to the expected exit time, the joint law of particles remain close to the law of independent non-linear McKean-Vlasov processes.
Keywords
Cite
@article{arxiv.2503.00157,
title = {Long-time propagation of chaos and exit times for metastable mean-field particle systems},
author = {Pierre Monmarché},
journal= {arXiv preprint arXiv:2503.00157},
year = {2025}
}