Vlasov limit for a chain of oscillators with Kac potentials

Alejandro Fernandez Montero (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We consider a chain of anharmonic oscillators with local mean field interaction and long-range stochastic exchanges of velocity. Even if the particles are not exchangeable, we prove the convergence of the empirical measure associated with this chain to a solution of a Vlasov-type equation. We then use this convergence to prove energy diffusion for a restricted class of anharmonic potentials.

Mots clés: Mean field limit; Vlasov equations; Kac potentials; Chain of oscillators

Domaines: Probabilités [math.PR]; Mécanique statistique [cond-mat.stat-mech]

Alejandro Fernandez Montero. Vlasov limit for a chain of oscillators with Kac potentials. 2020. ⟨hal-02957947⟩