{
  "abstract": "Recent work of the author investigates certain random processes, valued in abelian p-groups, that naturally arise in the study of Haar random matrices over $\\mathbb{Z}_p$. It was found, somewhat surprisingly, that these processes are reversible Markov chains. In this short note, we give a simple alternative derivation of this fact. The new derivation also proves that this phenomenon is not specific to $\\mathbb{Z}_p$, but generalizes to Haar random matrices over any profinite local ring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00134",
  "author_total": 1,
  "authors": [
    {
      "name": "Nikita Lvov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d0rdhr26sz13a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00134",
  "fulltext_url": null,
  "id": "d0rdhr26sz13a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00134",
  "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.NT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|advanced mathematical theories"
    ]
  ],
  "openalex": "W7216025868",
  "pdf_url": "https://arxiv.org/pdf/2610.00134",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d0rdhr26sz13a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00134",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00134"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Markov chains arising in the study of random matrices over pro-finite rings",
  "title_text": "Markov chains arising in the study of random matrices over pro-finite rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/d0rdhr26sz13a",
  "venue": "arXiv",
  "versions": []
}