Gradient flow structure for McKean-Vlasov equations on discrete spaces
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2016
- arXiv:
- arXiv:1601.08098
- Bibcode:
- 2016arXiv160108098E
- Keywords:
-
- Mathematics - Probability;
- 60J27 (Primary);
- 34A34;
- 49J40;
- 49J45 (Secondary)
- E-Print:
- Discrete and Continuous Dynamical Systems - Series A , Vol. 36, no. 12, December 2016