{
  "abstract": "Given a bivariate copula $C$, the bivariate copula $Ψ(C)$ is defined as the Markov product of $C^T$ and $C$. In this paper we consider the diagonal section of $Ψ(C)$ under the additional assumption that its value at a single point is known. We determine the exact upper and lower bounds for the diagonal section of $Ψ(C)$, given that $Ψ(C)(a,a)=d \\in [a^2,a]$, where $a \\in [0,1]$ is a fixed point. Furthermore, we describe some additional properties of the transformation $Ψ$, such as its behavior under ordinal sums and the survival operation. We also study checkerboard copulas in the range of $Ψ$ and matrices associated to them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13846",
  "author_total": 3,
  "authors": [
    {
      "name": "Roman Drnovšek"
    },
    {
      "name": "Damjana Kokol Bukovšek"
    },
    {
      "name": "Nik Stopar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2583bmk8gdxct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13846",
  "fulltext_url": null,
  "id": "2583bmk8gdxct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13846",
  "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.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7221540357",
  "pdf_url": "https://arxiv.org/pdf/2610.13846",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2583bmk8gdxct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13846",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13846"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On diagonal sections of Markov products of copulas",
  "title_text": "On diagonal sections of Markov products of copulas",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:46Z",
  "url": "https://research.draconitic.com/paper/2583bmk8gdxct",
  "venue": "arXiv",
  "versions": []
}