Gradient flow structure for McKean-Vlasov equations on discrete spaces

@article{Erbar2016GradientFS,
  title={Gradient flow structure for McKean-Vlasov equations on discrete spaces},
  author={Matthias Erbar and Max Fathi and Vaios Laschos and Andr{\'e} Schlichting},
  journal={Discrete and Continuous Dynamical Systems},
  year={2016},
  volume={36},
  pages={6799-6833}
}
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. 
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