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Gradient flow structure for McKean-Vlasov equations on discrete spaces

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  • 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.
    Mathematics Subject Classification: Primary: 60J27; Secondary: 34A34, 49J40, 49J45.

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