Captivity of mean-field systems

Julian Tugaut (1)

1 Universität Bielefeld = Bielefeld University

We investigate the exit time of some mean-field system which is related to McKean-Vlasov diffusions under convex interaction and double-well exterior force. In one hand, we show that the meta-potential which intervenes in the system admits a number of wells which tends to infinity when the number of particles tends to infinity. In the other hand, by using the convergence of the self-stabilizing processes, the phase transitions of the granular media equation, we show that there exist some traps such that the diffusion in $\mathbb{R}^N$ can not escape when $N$ tends to infinity. This means that in high dimension and with fixed noise, the meta-potential is not the function which drives the random dynamical system.

Domaines: Probabilités [math.PR]

Julian Tugaut. Captivity of mean-field systems. 2011. ⟨hal-00573047v1⟩