{
  "abstract": "We study the addition of two independent random $N\\times M$ rectangular matrices with invariant distributions in two limiting regimes, where the parameter $\\beta$ (inverse temperature) tends to infinity and $0$. In the low temperature regime the random singular values of the sum concentrate at deterministic points, while in the high temperature regime, we obtain a law of large numbers for the empirical measures. As a consequence, we obtain a duality between low and high temperatures. Our proof uses the type BC Bessel function as characteristic function of rectangular matrices, and through the analysis of this function we introduce a new family of cumulants, that linearize the addition in the high temperature limit, and degenerate to the classical and free cumulants in special cases.",
  "abstract_shown": true,
  "affiliations": [
    "USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jiaming Xu",
      "orcid": "0000-0001-6104-4742"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xzwc9n8pw14p.bib",
  "cited_by": 10,
  "doi": "10.3842/sigma.2026.053",
  "fulltext_url": null,
  "id": "7xzwc9n8pw14p",
  "issns": [
    "1815-0659"
  ],
  "landing_url": "https://doi.org/10.3842/sigma.2026.053",
  "language": "en",
  "licence": "CC-BY-SA",
  "licence_label": "CC BY-SA",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2613|Random Matrices and Applications"
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  "openalex": "W4361189022",
  "pdf_url": "https://sigma-journal.com/2026/053/sigma26-053.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-27",
  "publisher": "National Academy of Sciences of Ukraine",
  "ris": "https://research.draconitic.com/paper/7xzwc9n8pw14p.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4361189022",
      "source": "openalex",
      "url": "https://doi.org/10.3842/sigma.2026.053"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Random Matrices and Applications",
      "subfield": "statistics"
    }
  ],
  "title": "Rectangular Matrix Additions in Low and High Temperatures",
  "title_text": "Rectangular Matrix Additions in Low and High Temperatures",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/7xzwc9n8pw14p",
  "venue": "Symmetry Integrability and Geometry Methods and Applications",
  "versions": []
}