Commutators, mean-field, and supercritical mean-field limits for Coulomb/Riesz gases
Abstract
This paper is intended as a companion to the author's talk "Commutator estimates and mean-field limits for Coulomb/Riesz gases" at the 2025 Journ\'ees \'equations aux d\'eriv\'ees partielles in Aussois. The goal is to provide a concise, accessible account of sharp commutator estimates recently obtained for modulated energies associated to Coulomb/Riesz interactions and how these estimates lead to optimal results for mean-field and supercritical mean-field limits of Coulomb/Riesz gas dynamics via the modulated-energy method. The exposition centers on the works arXiv:2408.14642, arXiv:2407.15650 with Serfaty and arXiv:2511.13461, arXiv:2601.02326 with Hess-Childs and Serfaty.
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