Exit-time of mean-field particles system

International audienceThe 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 ℝd 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{2σ2HN}, HN being the exit-cost. We also show that this exit-cost converges to some quantity H