{
  "abstract": "We construct random hives from deformed GUE minor processes. Starting from two independent diagonally deformed GUE matrices \\[ X=\\sqrt{n}(wG+uD),\\qquad Y=\\sqrt{n}(w'G'+u'D'), \\] where \\(D,D'\\) are diagonal and have GUE spectra, we use their minor processes to form a double hive and then apply the octahedron recurrence. Under the matching condition \\[ \\frac{u}{w^2}=\\frac{u'}{(w')^2}, \\] we prove that the resulting hive law is close, in relative entropy, to a GUE hive law. More precisely, if \\[ a^2=w^2+u^2,\\qquad b^2=(w')^2+(u')^2, \\] then the produced hive density $q_n$ satisfies \\[ D_{\\mathrm{KL}}\\!\\left( q_n\\, \\middle\\|\\, \\operatorname{Density}\\bigl(H_n(a\\sqrt n,b\\sqrt n,c_{**}\\sqrt n)\\bigr) \\right) = O(n\\log n). \\] The third scale $c_{**}$ is determined by a limiting tetrahedral optimization problem; equivalently, writing \\(δ=u+u'\\), \\[ δ^2 = \\frac{ 2c_{**}^4(c_{**}^2-a^2-b^2) }{ (c_{**}^2-a^2+b^2)(c_{**}^2+a^2-b^2) }. \\] Thus the construction realizes GUE hive laws, up to subleading relative entropy, throughout the right-angled and obtuse regime. The introduction records two explicit surface-tension approximations and numerical comparisons which motivated the construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04138",
  "author_total": 1,
  "authors": [
    {
      "name": "Hariharan Narayanan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3bx18mtvmpzy3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04138",
  "fulltext_url": null,
  "id": "3bx18mtvmpzy3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04138",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7167631607",
  "pdf_url": "https://arxiv.org/pdf/2607.04138",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3bx18mtvmpzy3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2607.04138",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04138"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Hives from deformed GUE minor processes",
  "title_text": "Hives from deformed GUE minor processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/3bx18mtvmpzy3",
  "venue": "arXiv",
  "versions": []
}