{
  "abstract": "We consider the family ${\\mathcal{C}}_d^{Π_{d-1}}$ of all $d$-dimensional copulas whose $(d-1)$-dimensional marginals are all equal to the $(d-1)$-dimensional product copula $Π_{d-1}$ and tackle the natural question, `how far away' from the $d$-dimensional product copula $Π_d$ elements in ${\\mathcal{C}}_d^{Π_{d-1}}$ can be. We provide definitive answers for both, the uniform metric $d_\\infty$ as well as the stronger, conditioning-based metric $D_1$. The established results clearly indicate that the family ${\\mathcal{C}}_d^{Π_{d-1}}$ is larger than one might expect.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Statistics and Probability Letters 240 (2027)",
  "arxiv": "2608.18286",
  "author_total": 3,
  "authors": [
    {
      "name": "Damjana Kokol Bukovšek"
    },
    {
      "name": "Nik Stopar"
    },
    {
      "name": "Wolfgang Trutschnig"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b74xg4jatpqem.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18286",
  "fulltext_url": null,
  "id": "b74xg4jatpqem",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18286",
  "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.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.18286",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b74xg4jatpqem.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2608.18286",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18286"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "How far are $d$-dimensional copulas with uniform $(d-1)$-marginals from (total) independence?",
  "title_text": "How far are d-dimensional copulas with uniform (d−1)-marginals from (total) independence?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:36Z",
  "url": "https://research.draconitic.com/paper/b74xg4jatpqem",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.spl.2026.110948",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}