2025/02/28 by Pierre Monmarché, Monmarché, Pierre · 2 citations
Environmental Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Ecosystem dynamics and resilience #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2503.00157
openalex publication_date 2025/02/28 · openalex created_date 2025/10/12 · openalex updated_date 2026/08/01
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.