{
  "abstract": "We prove convergence to critical Gaussian multiplicative chaos for characteristic-polynomial measures of complex iid matrices. Let $A_N=N^{-1/2}(ξ_{ij})$, with a fixed law satisfying $\\mathbb Eξ=\\mathbb Eξ^2=0$, $\\mathbb E|ξ|^2=1$, and finite moments of every order; no density is assumed. On each fixed disk $\\{|z|\\le r\\}$, $0<r<1$, expectation-normalized determinant measures at power $2\\sqrt2$, multiplied by $\\sqrt{\\tfrac12\\log N}$, converge to critical chaos with a fourth-cumulant covariance correction. The normalized height-deficit marked measure converges to the product of this spatial limit and the standard Rayleigh law. Convergence holds jointly with centered averages of the $\\sqrt2$-scaled original logarithmic field against finitely many smooth compactly supported bulk tests, and with the two-sided near-critical curve at powers $q=2\\sqrt2-2λ/\\sqrt{\\log N}$. On fixed compact parameter intervals, the curve converges in law in the uniform weak topology; all limiting coordinates use the same Gaussian field. The limiting curve is an explicit deterministic profile times the same critical measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01794",
  "author_total": 3,
  "authors": [
    {
      "name": "Yin Cai"
    },
    {
      "name": "Xiang Fang"
    },
    {
      "name": "Feng Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1t5x3hr04rgh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01794",
  "fulltext_url": null,
  "id": "f1t5x3hr04rgh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01794",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01794",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1t5x3hr04rgh.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01794",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01794"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Critical characteristic-polynomial chaos for complex iid matrices",
  "title_text": "Critical characteristic-polynomial chaos for complex iid matrices",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/f1t5x3hr04rgh",
  "venue": "arXiv",
  "versions": []
}