Gradient flow structure for McKean-Vlasov equations on discrete spaces

Matthias Erbar, Max Fathi, Vaios Laschos, André Schlichting

Published 2016-01-29Version 1

In this work, we show that a family of non-linear mean-field equations on discrete spaces, can be viewed as a gradient flow of a natural free energy functional with respect to a certain metric structure we make explicit. We also prove that this gradient flow structure arises as the limit of the gradient flow structures of a natural sequence of N-particle dynamics, as N goes to infinity.