{"paper":{"title":"Convergence rate for Fluctuations of mean field interacting diffusion and application to 2D viscous Vortex model and Coulomb potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alekos Cecchin, Paul Nikolaev","submitted_at":"2025-09-01T08:54:42Z","abstract_excerpt":"For a system of mean field interacting diffusion on $\\mathbb{T}^d$, the empirical measure $\\mu^N$ converges to the solution $\\mu$ of the Fokker-Planck equation. Refining this mean field limit as a Central Limit Theorem, the fluctuation process $\\rho^N_t= \\sqrt{N}( \\mu^N_t -\\mu_t)$ convergences to the solution $\\rho$ of a linear stochastic PDE on the negative Sobolev space $H^{-\\lambda-2}(\\mathbb{T}^d)$. The main result of the paper is to establish a rate for such convergence: we show that $|\\mathbb{E}[\\Phi(\\rho_t^N)] - \\mathbb{E}[\\Phi(\\rho_t)]| = \\mathcal{O}(\\tfrac{1}{\\sqrt{N}})$, for smooth f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01266","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.01266/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}