{
  "abstract": "We study the normalized half moment $α_{\\mathbb R}^{(λ)}(N)$ of the size-$N$ Laguerre orthogonal ensemble for real shape $λ\\ge0$. At integer shape this is the expected average singular value of an $N\\times(N+λ)$ real Gaussian matrix. The square mean increases with the dimension, whereas every real shape $λ\\ge1$ decreases. Between these two regimes the decrement is strictly increasing in $λ$, and hence has a unique zero in $(0,1)$ for every $N$. There is also a unique crossing of the Marchenko--Pastur limit. Both thresholds converge to $λ_*=1-π/4$, and their first corrections show that they separate on the scale $(\\log N)/N$. The proof starts from an exact decomposition of the real half moment into its complex counterpart and a positive orthogonal correction. Recent unitary estimates take care of the complex term. An Abel completion, together with a Laguerre connection formula, turns the orthogonal correction into a positive diagonal series; the square case, the regime $λ\\ge1$, and the transition can then all be read from this same series.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.12151",
  "author_total": 1,
  "authors": [
    {
      "name": "Ondrej Hutník"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9y99ef7qvj7h5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.12151",
  "fulltext_url": null,
  "id": "9y99ef7qvj7h5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.12151",
  "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.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7202353764",
  "pdf_url": "https://arxiv.org/pdf/2608.12151",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9y99ef7qvj7h5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2608.12151",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.12151"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Dimension Monotonicity in Laguerre Ensembles II: Average Singular Values and the Rectangularity Transition in the Orthogonal Case",
  "title_text": "Dimension Monotonicity in Laguerre Ensembles II: Average Singular Values and the Rectangularity Transition in the Orthogonal Case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/9y99ef7qvj7h5",
  "venue": "arXiv",
  "versions": []
}