The hydrodynamic limit for local mean-field dynamics with unbounded spins

TL;DR

This paper proves that the empirical measure of certain unbounded spin systems converges to a McKean-Vlasov equation in the hydrodynamic limit, extending previous results to more general interactions.

Contribution

It extends the hydrodynamic limit and propagation of chaos results to unbounded spin systems with local mean field interactions, beyond bounded spins.

Findings

Empirical measures converge to McKean-Vlasov solutions

Propagation of chaos is established for unbounded spins

Generalizes previous bounded spin results

Abstract

We consider the dynamics of a class of spin systems with unbounded spins interacting with local mean field interactions. We proof convergence of the empirical measure to the solution of a McKean-Vlasov equation in the hydrodynamic limit and propagation of chaos. This extends earlier results of G\"artner, Comets and others for bounded spins or strict mean field interactions.