{
  "abstract": "We extend the spherical-integral approach to $\\mathcal{R}$-transforms of non-Hermitian random matrices to random matrices with a fixed $K \\times K$ block structure. We introduce a rank-$K$ spherical integral defining a scalar $H$-transform on $2K \\times 2K$ overlap matrices and an associated matrix-valued $\\mathcal{R}$-transform encoding the joint block structure. Using the replica method, we derive a conjectural subordination relation for sums of independent block matrices. This framework provides a method for determining the spectral boundaries of large non-Hermitian random matrices with a fixed block structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31730",
  "author_total": 1,
  "authors": [
    {
      "name": "Pierre Bousseyroux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bhm6rb83fdh3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31730",
  "fulltext_url": null,
  "id": "7bhm6rb83fdh3",
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  "landing_url": "https://arxiv.org/abs/2609.31730",
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "cond-mat.dis-nn"
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      "arxiv",
      "math-ph"
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      "2613|Random Matrices and Applications"
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  "openalex": "W7214746084",
  "pdf_url": "https://arxiv.org/pdf/2609.31730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bhm6rb83fdh3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.31730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31730"
    }
  ],
  "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": "R-transforms for non-Hermitian block random matrices: a spherical integral approach",
  "title_text": "R-transforms for non-Hermitian block random matrices: a spherical integral approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/7bhm6rb83fdh3",
  "venue": "arXiv",
  "versions": []
}