WIAS Preprint No. 2219, (2016)

Gradient flow structure for McKean--Vlasov equations on discrete spaces



Authors

  • Erbar, Matthias
  • Fathi, Max
  • Laschos, Vaios
  • Schlichting, André

2010 Mathematics Subject Classification

  • 34A34 49J40 49J45 49Q20 60J25 60J27

Keywords

  • Gradient flow structure, weakly interacting particles systems, nonlinear Markov chains, mean-field limit, evolutionary Gamma-convergence, transportation metric

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

Appeared in

  • Discrete Contin. Dyn. Syst., 36 (2016), pp. 6799--6833.

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