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arXiv · 2605.28979

Singular mean-field limits for fluctuations around equilibrium

Mitia Duerinckx·Pierre-Emmanuel Jabin
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Abstract

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.

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Mitia Duerinckx, Pierre-Emmanuel Jabin. 2026-05-27. Singular mean-field limits for fluctuations around equilibrium. https://arxiv.org/abs/2605.28979

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