Gradient flow structure for McKeanVlasov equations on discrete spaces
Abstract
In this work, we show that a family of nonlinear meanfield 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 Nparticle dynamics, as N goes to infinity.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.08098
 Bibcode:
 2016arXiv160108098E
 Keywords:

 Mathematics  Probability;
 60J27 (Primary);
 34A34;
 49J40;
 49J45 (Secondary)
 EPrint:
 Discrete and Continuous Dynamical Systems  Series A , Vol. 36, no. 12, December 2016