Gradient flow structure for McKean-Vlasov equations on discrete spaces
Probability
2016-10-26 v2
Abstract
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.
Cite
@article{arxiv.1601.08098,
title = {Gradient flow structure for McKean-Vlasov equations on discrete spaces},
author = {Matthias Erbar and Max Fathi and Vaios Laschos and André Schlichting},
journal= {arXiv preprint arXiv:1601.08098},
year = {2016}
}