{
  "abstract": "We prove a logarithmic central limit theorem for a tagged particle in infinite-dimensional Dyson Brownian motion at inverse temperature $β=2$, starting from the sine$_2$ point process. The fluctuation is of order $\\sqrt{\\log t}$, which is subdiffusive and substantially slower than the polynomial fluctuations of classical short-range interacting particle systems, reflecting the rigidity induced by long-range logarithmic repulsion. We further identify the scaling limit as the singular Gaussian field corresponding to the zero-Hurst parameter, which provides a realisation of the singular Gaussian field as a scaling limit of a tagged particle raised by Dürr, Goldstein and Lebowitz (Comm. Pure Appl. Math. 38 (1985)).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08365",
  "author_total": 2,
  "authors": [
    {
      "name": "Hirofumi Osada"
    },
    {
      "name": "Kohei Suzuki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hc3hs13q85av.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08365",
  "fulltext_url": null,
  "id": "8hc3hs13q85av",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08365",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08365",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hc3hs13q85av.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.08365",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08365"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The singular Gaussian scaling limit for a tagged particle in the infinite-dimensional Dyson model at $β=2$",
  "title_text": "The singular Gaussian scaling limit for a tagged particle in the infinite-dimensional Dyson model at β=2",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/8hc3hs13q85av",
  "venue": "arXiv",
  "versions": []
}