{
  "abstract": "Using contour-integral representations of the permanent and of the Hafnian, we turn the computation of their moments for random matrices into a replica calculation, analogous to that of the moments of the partition function of a mean-field spin glass. For the $2k$-th moment of $N\\times N$ matrices with independent entries, the dominant saddle point is replica symmetric for $k>2$, and we obtain in closed form the exponential growth rate, the prefactor and the first $1/N$ correction, in agreement with exact enumerations. The growth rate depends only on whether the entries are real or complex; higher cumulants affect only the prefactor and the $1/N$ term. At $k=2$ the replica-symmetric solution becomes unstable, separating a power-law bulk of the distribution from a large-deviation tail, which we compute. The results apply to boson sampling with single photons and with squeezed light.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27872",
  "author_total": 5,
  "authors": [
    {
      "name": "Paolo Facchi"
    },
    {
      "name": "Angelo Mariano"
    },
    {
      "name": "Giorgio Parisi"
    },
    {
      "name": "Saverio Pascazio"
    },
    {
      "name": "Antonello Scardicchio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8480zf6ekcyn7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27872",
  "fulltext_url": null,
  "id": "8480zf6ekcyn7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27872",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7223084987",
  "pdf_url": "https://arxiv.org/pdf/2610.27872",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8480zf6ekcyn7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27872",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27872"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Moments of Random Permanents and Hafnians: A Replica Approach",
  "title_text": "Moments of Random Permanents and Hafnians: A Replica Approach",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:17Z",
  "url": "https://research.draconitic.com/paper/8480zf6ekcyn7",
  "venue": "arXiv",
  "versions": []
}