{
  "abstract": "We introduce a left $G$-circulant decomposition for matrices indexed by an arbitrary finite group $G$, extending the diagonal decomposition associated with cyclic groups. We show that, when $A\\in M_{|G|}(\\mathcal A)$ is free from $M_{|G|}(\\mathbb C)$, the components arising from the left $G$-circulant decomposition of $A^t$ form a free family, with the components associated with inverse pairs forming $R$-diagonal pairs. We also describe the distributions of these components in terms of the distribution of $A$. Our results recover the cyclic case and show that different group structures of the same order may lead to different free decompositions of the same matrix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09648",
  "author_total": 2,
  "authors": [
    {
      "name": "Octavio Arizmendi"
    },
    {
      "name": "Julian Zazueta-Obeso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0nhex5wt9f06a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09648",
  "fulltext_url": null,
  "id": "0nhex5wt9f06a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09648",
  "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.OA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7212195256",
  "pdf_url": "https://arxiv.org/pdf/2609.09648",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0nhex5wt9f06a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09648",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09648"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Freeness for the $G$-circulant Decomposition of the Partial Transpose of Random Matrices",
  "title_text": "Freeness for the G-circulant Decomposition of the Partial Transpose of Random Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/0nhex5wt9f06a",
  "venue": "arXiv",
  "versions": []
}