{
  "abstract": "We consider beta-Dyson Brownian motion, with $β>= 1$, started from a deterministic configuration with uniformly bounded support. Let $μ_t$ be the semicircular free-convolution flow issued from the initial empirical measure, and set $S_t = supp(μ_t)$. For every fixed $T, ε> 0$, with probability at least $1 - C \\exp(-(log n)^2)$, every particle remains within an epsilon-neighborhood of $S_t$ for all $0 <= t <= T$. The result holds from time zero, requires no regularity assumption at the initial spectral edges, and applies to multi-cut supports with macroscopic interior gaps. A key ingredient is a deterministic local resolvent exclusion principle: an $o((n η)^(-1))$ comparison of Stieltjes transforms on a complex disc above a real point separated from the reference support excludes eigenvalues from the corresponding real interval. This gives a model-independent mechanism for converting local resolvent estimates into spectral confinement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01770",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiaoyang Huang"
    },
    {
      "name": "Shengjing Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0yth7ketmm4vv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01770",
  "fulltext_url": null,
  "id": "0yth7ketmm4vv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01770",
  "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",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7207567122",
  "pdf_url": "https://arxiv.org/pdf/2609.01770",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0yth7ketmm4vv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.01770",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01770"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Support of Dyson Brownian Motion",
  "title_text": "Support of Dyson Brownian Motion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/0yth7ketmm4vv",
  "venue": "arXiv",
  "versions": []
}