Mean field limit for Coulomb-type flows

By Sylvia Serfaty, appendix with Mitia Duerinckx. Duke mathematical journal, 2018

184 citations recorded by the source corpus.

We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary dimension. The proof is based on a modulated energy method using a Coulomb or Riesz distance, assumes that the solutions of the limiting equation are regular enough and exploits a weak-strong stability property for them. The method can handle the addition of a regular interaction kernel, and applies also to conservative and mixed flows. In the appendix, it is also adapted to prove the mean-field convergence of the solutions to Newton's law with Coulomb or Riesz interaction in the monokinetic case to solutions of an Euler-Poisson type system.

Subfields: Applied Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/4aafcdf5ba119c981bb004699c2dcd191c7970fd

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Citations in the corpus

Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions (2021, background): “It is natural to wonder, though, if our general strategy of comparing the k-particle “energy” to the (k+1)-particle “energy” via the BBGKY hierarchy could be adapted for different kinds of dynamics and perhaps better-tailored notions of “energies,” rather than entropy, such as the modulated (free) e”
Distribution dependent SDEs driven by additive fractional Brownian motion (2021, methodology): “On the one hand, new methods based on entropy inequalities [6, 14, 28] and modulated energy methods [41, 42] have allowed for the rigorous derivation of mean field limits for fairly singular B; while on the other, DDSDEs with irregular drifts are related to the flourishing field of regularization by”