{
  "abstract": "We study the large-$N$ asymptotics of a constrained spherical integral for non-Hermitian random matrices, in which the norms and mutual scalar product of two vectors are fixed. In the delocalized regime, the asymptotics are governed by the non-Hermitian transforms $\\mathcal R_1$ and $\\mathcal R_2$. At saddle-point level, the constrained integral exhibits a transition to a localized regime controlled by the largest singular value of a shifted matrix and by the overlap of its associated left and right singular vectors. Motivated by the Hermitian spherical-integral mechanism and by the Coulomb-gas picture, we formulate conjectures for one-eigenvalue large deviations and boundary fluctuations. Throughout, our analysis is carried out in the spirit of mathematical physics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20685",
  "author_total": 2,
  "authors": [
    {
      "name": "Pierre Bousseyroux"
    },
    {
      "name": "Marc Potters"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ws5bdatgfta6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20685",
  "fulltext_url": null,
  "id": "6ws5bdatgfta6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20685",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7213588596",
  "pdf_url": "https://arxiv.org/pdf/2609.20685",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ws5bdatgfta6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.20685",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20685"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Phase transitions in non-Hermitian spherical integrals",
  "title_text": "Phase transitions in non-Hermitian spherical integrals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/6ws5bdatgfta6",
  "venue": "arXiv",
  "versions": []
}