Exit-time of mean-field particles system

Julian Tugaut (1)

1 PSPM - Probabilités, statistique, physique mathématique

The current article is devoted to the study of a mean-field system of particles. The question that we are interested in is the behaviour of the exit-time of the first particle (and the one of any particle) from a domain D on R d as the diffusion coefficient goes to 0. We establish a Kramers'type law. In other words, we show that the exit-time is exponentially equivalent to exp 2 σ 2 H N , H N being the exit-cost. We also show that this exit-cost converges to some quantity H. To obtain this result, we proceed by two different approaches.

Mots clés: Exit-problem; Large deviations; Interacting particle systems; Mean-field systems

Domaines: Probabilités [math.PR]

Julian Tugaut. Exit-time of mean-field particles system. 2017. ⟨hal-01611394⟩