{
  "abstract": "The $Λ$-distribution of a compact matrix group is an invariant in algebraic probability theory that was recently introduced to study zero distributions of function field $L$-functions. It is encoded by the $σ$-moment generating function, a generalization of the Molien series of classical invariant theory. In this work, we compute the $σ$-moment generating functions of finite matrix groups in many new cases. In particular, we compute the asymptotic $Λ$-distributions for the infinite families of Weyl reflection groups of types $B_n/C_n$ and $D_n$, complementing the previously known case of reflection groups of type $A_n$, i.e., symmetric groups. We also establish a general result relating the shapes of $σ$-moment generating functions to the distributions of associated classical random variables, explaining a previous ad hoc observation for independent Gaussians arising from traces of powers on compact classical groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.16796",
  "author_total": 10,
  "authors": [
    {
      "name": "Matthew Bertucci"
    },
    {
      "name": "Sam Van Blarcom"
    },
    {
      "name": "Benjamin Glancy"
    },
    {
      "name": "Sean Howe"
    },
    {
      "name": "Thomas Madden"
    },
    {
      "name": "Ben Miller"
    },
    {
      "name": "Souparna Pal"
    },
    {
      "name": "Giorgos Papagrigoriou"
    },
    {
      "name": "Nathan Raikman"
    },
    {
      "name": "Tien Tran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8g2bdsbpzmswj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.16796",
  "fulltext_url": null,
  "id": "8g2bdsbpzmswj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.16796",
  "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",
      "math.AC"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7203675221",
  "pdf_url": "https://arxiv.org/pdf/2608.16796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8g2bdsbpzmswj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2608.16796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.16796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Matrix group $Λ$-distributions",
  "title_text": "Matrix group Λ-distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/8g2bdsbpzmswj",
  "venue": "arXiv",
  "versions": []
}