{
  "abstract": "We study products of independent Haar matrices interspersed with a fixed corank-one projection. As the matrix dimension $N$ and product length $L$ grow with $L/N\\toτ$, we prove that the empirical distribution of squared singular values converges to the free multiplicative Poisson law with $S$-transform $S(z)=\\exp(τ/(1+z))$, for both the unitary and orthogonal ensembles. Lagrange inversion yields its moments explicitly, proving Beenakker's conjectured Erlang formula for every moment order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.05693",
  "author_total": 1,
  "authors": [
    {
      "name": "Joon Hyung Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/66amw6p6xzs20.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.05693",
  "fulltext_url": null,
  "id": "66amw6p6xzs20",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.05693",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
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      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7167696421",
  "pdf_url": "https://arxiv.org/pdf/2607.05693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/66amw6p6xzs20.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:23Z",
      "native_id": "2607.05693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.05693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Double-Scaling Limits for Monitored Haar Products",
  "title_text": "Double-Scaling Limits for Monitored Haar Products",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:37Z",
  "url": "https://research.draconitic.com/paper/66amw6p6xzs20",
  "venue": "arXiv",
  "versions": []
}