Singular mean-field limits for fluctuations around equilibrium
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914609781276672 |
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| author | Duerinckx, Mitia Jabin, Pierre-Emmanuel |
| author_facet | Duerinckx, Mitia Jabin, Pierre-Emmanuel |
| contents | This work addresses the mean-field limit of inertial particle systems with singular interactions in a perturbative regime around Gibbs equilibrium. We prove that small fluctuations around equilibrium are asymptotically governed by the linearized Vlasov equation. The result applies to a broad class of singular interaction kernels, including the Coulomb case in dimensions $d\le3$. In particular, this provides a rigorous derivation of the linearized mean-field dynamics near equilibrium in settings where the corresponding nonlinear mean-field limit remains out of reach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28979 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singular mean-field limits for fluctuations around equilibrium Duerinckx, Mitia Jabin, Pierre-Emmanuel Analysis of PDEs Mathematical Physics Probability This work addresses the mean-field limit of inertial particle systems with singular interactions in a perturbative regime around Gibbs equilibrium. We prove that small fluctuations around equilibrium are asymptotically governed by the linearized Vlasov equation. The result applies to a broad class of singular interaction kernels, including the Coulomb case in dimensions $d\le3$. In particular, this provides a rigorous derivation of the linearized mean-field dynamics near equilibrium in settings where the corresponding nonlinear mean-field limit remains out of reach. |
| title | Singular mean-field limits for fluctuations around equilibrium |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2605.28979 |