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Gradient flow structure for McKean-Vlasov equations on discrete spaces
Matthias Erbara, Max Fathib c d, Vaios Laschose, André Schlichtingb c d
- aDepartment of Mathematics - University of Bonn
- bUniversity of Bonn, Germany
- cUniversity of California, Berkeley
- dWeierstrass Institute
- eDepartment of Mathematics [Berkeley]
Discrete and Continuous Dynamical SystemsAmerican Institute of Mathematical Sciences2016-01-01 42 citations50 references
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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.