Phase transitions of McKean-Vlasov processes in double-wells landscape

Julian Tugaut (1)

1 Universität Bielefeld = Bielefeld University

We prove under simple assumptions that there exist several phases for the self-stabilizing processes in a non-convex landscape. When the coefficient of diffusion is small, there are at least three stationary measures and when it is sufficiently large, there is a unique one. The non-uniqueness in small noise has already been proved in [Herrmann, Tugaut|2010] when the landscape is symmetric. Here, we will extend it in two directions: when the confining potential $V$ is not symmetric and when the interacting potential $F$ is not quadratic. The critical value will also be studied.

Domaines: Probabilités [math.PR]

Julian Tugaut. Phase transitions of McKean-Vlasov processes in double-wells landscape. 2011. ⟨hal-00573046v2⟩