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arXiv · 1601.08098

Gradient flow structure for McKean-Vlasov equations on discrete spaces

Matthias Erbar·Max Fathi·Vaios Laschos·André Schlichting
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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.

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Matthias Erbar, Max Fathi, Vaios Laschos, André Schlichting. 2016-01-29. Gradient flow structure for McKean-Vlasov equations on discrete spaces. https://doi.org/10.3934/dcds.2016096

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