{
  "abstract": "We study metastability and long-time propagation-of-chaos for mean-field interacting diffusions on the circle with multiple local free-energy minima. Working modulo rotations, we identify sharp exponential time scales for metastability and the validity and breakdown of the McKean-Vlasov approximation. Assuming finitely many critical rotation orbits and distinct local-minimum energies, we show that, for initial data in the attraction basin of a nonglobal minimum, metastability and propagation-of-chaos hold uniformly over deterministic times up to $e^{N(D-\\varepsilon)}$ and fail at every deterministic sequence growing faster than $e^{N(D+\\varepsilon)}$. Here $N$ is the particle number and $D$ the depth of the maximal Freidlin-Wentzell energy cycle having that minimum as its bottom. The same threshold governs running averages of the squared approximation error in a stronger pathwise sense, with corresponding metastability and propagation-of-chaos bounds for suitably aligned time-averaged empirical measures. When the global-minimum orbit is unique, we establish uniform-in-time propagation-of-chaos in its attraction basin without assuming finitely many critical orbits. The proofs develop the Freidlin-Wentzell cycle analysis for the empirical measure process and exploit Dawson and Gärtner's fixed-horizon large deviation estimates to analyze long excursions between metastable wells. We give a checkable Fourier criterion for finiteness of the critical orbits. We also investigate connections with phase transitions in the free-energy landscape, and discuss applications to the noisy Kuramoto and noisy transformer models. We provide, to our knowledge, the first sharp exponential-time analysis of the Dawson-Gärtner `tunnelling phenomenon' for general smooth interactions, with two-sided probability bounds and matching propagation-of-chaos thresholds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08755",
  "author_total": 1,
  "authors": [
    {
      "name": "Sayan Banerjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60vr1skzdmqqy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08755",
  "fulltext_url": null,
  "id": "60vr1skzdmqqy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08755",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220977470",
  "pdf_url": "https://arxiv.org/pdf/2610.08755",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60vr1skzdmqqy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.08755",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08755"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Metastability and Sharp Propagation-of-Chaos Thresholds for Mean-Field Interacting Diffusions on the Circle",
  "title_text": "Metastability and Sharp Propagation-of-Chaos Thresholds for Mean-Field Interacting Diffusions on the Circle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/60vr1skzdmqqy",
  "venue": "arXiv",
  "versions": []
}