{
  "abstract": "We study the joint diffusive-mean field limit for a system of weakly interacting kinetic Langevin dynamics, extending the results of Delgadino, Gvalani and Pavliotis (Arch. Ration. Mech. Anal., 2021) to the hypoelliptic/hypocoercive case. We show that, in the absence of phase transitions, the two limits commute, and we calculate the covariance matrix of the limiting Brownian motion using the Green-Kubo/Kipnis-Varadhan formula. However, at low temperatures, and in the presence of phase transitions, the two limits may not commute. We demonstrate our findings by providing a detailed analysis of the diffusive-mean field limit for the $O(2)$ model in a magnetic field. Our analysis is based on the systematic use of recently developed hypocoercivity techniques, together with an appropriate linearization of the mean field McKean-Vlasov-Fokker-Planck partial differential equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.15896",
  "author_total": 4,
  "authors": [
    {
      "name": "Raphaël Gastaldello"
    },
    {
      "name": "Grigorios A. Pavliotis"
    },
    {
      "name": "Gabriel Stoltz"
    },
    {
      "name": "Urbain Vaes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmy52c5c7fxh1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.15896",
  "fulltext_url": null,
  "id": "cmy52c5c7fxh1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.15896",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7169752689",
  "pdf_url": "https://arxiv.org/pdf/2607.15896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmy52c5c7fxh1.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:13Z",
      "native_id": "2607.15896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.15896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the diffusive-mean field limit of a kinetic weakly interacting particle system",
  "title_text": "On the diffusive-mean field limit of a kinetic weakly interacting particle system",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/cmy52c5c7fxh1",
  "venue": "arXiv",
  "versions": []
}