{
  "abstract": "Consider the hyperbolic Gaussian analytic function (GAF) \\begin{equation*} F_{\\mathbb{D}}(z)=\\sum_{n=0}^{\\infty }ξ_{n}z^{n},\\qquad |z|<1, \\end{equation*} where the $ξ_{n}$ are independent standard complex Gaussian variables. Peres-Virág theorem tells that the distribution of the zeros of $F_{\\mathbb{D}}(z)$ is provided by a Determinantal Point Process (DPP). We prove that $F_{\\mathbb{D}}(z)$ is the only GAF whose zeros are determinantal with a Hermitian kernel, up to multiplication by a zero-free holomorphic function and a one-to-one holomorphic change of variable, with a \\ non-degeneracy condition imposed to exclude trivial cases. The proof identifies a geometric property of GAF's with (local) determinantal zeros: the metric defined by the first intensity must have constant curvature $-4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03118",
  "author_total": 1,
  "authors": [
    {
      "name": "Luís Daniel Abreu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/exp6qe2cz9b1x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03118",
  "fulltext_url": null,
  "id": "exp6qe2cz9b1x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03118",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03118",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/exp6qe2cz9b1x.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03118",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03118"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Rigidity of the Peres-Virág class",
  "title_text": "Rigidity of the Peres-Virág class",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/exp6qe2cz9b1x",
  "venue": "arXiv",
  "versions": []
}