Commutators, mean-field, and supercritical mean-field limits for Coulomb/Riesz gases
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910038184951808 |
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| author | Rosenzweig, Matthew |
| author_facet | Rosenzweig, Matthew |
| contents | 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 arXiv:2408.14642, arXiv:2407.15650 with Serfaty and arXiv:2511.13461, arXiv:2601.02326 with Hess-Childs and Serfaty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02169 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Commutators, mean-field, and supercritical mean-field limits for Coulomb/Riesz gases Rosenzweig, Matthew Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Probability 35Q70, 35Q35, 35Q83, 82C22, 82C70, 76B47 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 arXiv:2408.14642, arXiv:2407.15650 with Serfaty and arXiv:2511.13461, arXiv:2601.02326 with Hess-Childs and Serfaty. |
| title | Commutators, mean-field, and supercritical mean-field limits for Coulomb/Riesz gases |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Probability 35Q70, 35Q35, 35Q83, 82C22, 82C70, 76B47 |
| url | https://arxiv.org/abs/2603.02169 |