{
  "abstract": "We give non-asymptotic operator-norm tail bounds for random multi-matrix models with quadratic plus globally Lipschitz interactions. More precisely, let $μ_f$ be the probability measure on $(\\mathbb{M}_n)_{\\operatorname{sa}}^m$ with density proportional to $\\exp(-n^2(\\lVert x \\rVert_2^2/2+f(x)))$. If $f$ is $L$-Lipschitz with respect to $\\lVert \\cdot \\rVert_1$, we construct a coupling of $X\\simμ_f$ and an $m$-tuple $Z$ of independent GUE matrices such that $\\lVert X-Z \\rVert_\\infty\\leq L$ almost surely, where $\\lVert \\cdot \\rVert_\\infty$ is the maximum of the operator norms of the matrix tuple. This is an operator-norm analog of the $L^\\infty$-Wasserstein bound of Khudiakova, Maas, and Pedrotti (2025). We give a new proof based on the variational formula of Boué and Dupuis (1998), the associated Hamilton--Jacobi--Bellman equation, and the duality between entropy and pressure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05660",
  "author_total": 2,
  "authors": [
    {
      "name": "Charles-Philippe Diez"
    },
    {
      "name": "David Jekel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1m9kz1z6q8efa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05660",
  "fulltext_url": null,
  "id": "1m9kz1z6q8efa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05660",
  "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",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7220655024",
  "pdf_url": "https://arxiv.org/pdf/2610.05660",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1m9kz1z6q8efa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05660",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05660"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A tail bound for multi-matrix models with Lipschitz interaction",
  "title_text": "A tail bound for multi-matrix models with Lipschitz interaction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1m9kz1z6q8efa",
  "venue": "arXiv",
  "versions": []
}