Propagation of chaos for topological models without regularity

Abstract

We prove propagation of chaos for the mean-field limit of microscopic models with topological interactions without any regularity condition. The lack of regularity makes describing collective behavior for biological groups by these systems more feasible. We prove the convergence of marginals of solutions to the Liouville equation, associated with the dynamics issued from chaotic initial conditions, to some (tensorial powers of) solutions to the associated Vlasov limit equation for which uniqueness of solutions is not guaranteed a priori, due to the lack of regularity.