Commutators, mean-field, and supercritical mean-field limits for Coulomb/Riesz gases

Matthew Rosenzweig

doi:10.5802/jedp.698

Commutators, mean-field, and supercritical mean-field limits for Coulomb/Riesz gases
[Commutateurs, limite de champ moyen et limite de champ moyen supercritique pour les gaz de Coulomb/Riesz]

Matthew Rosenzweig ¹

¹Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA, USA

Journées équations aux dérivées partielles (2025), Exposé no. 7, 32 p.

Abstract (VO)
Résumé

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 Journées équations aux dérivées 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 [129, 131] with Serfaty and [84] with Hess-Childs and Serfaty.

Cet article est un complément à l’exposé de l’auteur intitulé « Commutator estimates and mean-field limits for Coulomb/Riesz gases », présenté aux Journées Équations aux Dérivées Partielles 2025 à Aussois. L’objectif est de fournir une présentation concise et accessible des estimations fines de commutateurs récemment obtenues pour les énergies modulées associées aux interactions de type Coulomb/Riesz, ainsi que d’expliquer comment ces estimations conduisent à des résultats optimaux pour les limites de champ moyen et de champ moyen supercritique de la dynamique des gaz de Coulomb/Riesz, via la méthode de l’énergie modulée. L’exposé s’appuie principalement sur les travaux [129, 131] avec Serfaty et [84] avec Hess-Childs et Serfaty.

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Publié le : 2026-06-19

DOI : 10.5802/jedp.698

Classification : 35Q70, 35Q35, 35Q83, 82C22, 82C70, 76B47
Keywords: Commutator estimates, modulated energy, mean-field limit, Riesz interactions, supercritical mean-field limit
Mots-clés : Estimations de commutateur, énergie modulée, limite de champ moyen, interactions de Riesz, limite de champ moyen supercritique

Affiliations des auteurs :

Matthew Rosenzweig ¹

¹ Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA, USA

Matthew Rosenzweig. Commutators, mean-field, and supercritical mean-field limits for Coulomb/Riesz gases. Journées équations aux dérivées partielles (2025), Exposé no. 7, 32 p.. doi: 10.5802/jedp.698

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