{
  "abstract": "Let $Π$ denote the independence copula and $M,W$ the upper and lower Fréchet--Hoeffding copulas. Catalano and Lavenant (2025) conjectured that $M$ and $W$ maximize the quadratic Wasserstein distance from $Π$ among all bivariate copulas. We prove this conjecture and characterize all equality cases: $\\mathcal W_2^2(C,Π)\\leq 1/10$, with equality if and only if $C\\in\\{M,W\\}$. We also determine explicitly the optimal Monge map from $Π$ to $M$. The proof is constructive and combines the optimal transport from independence to the diagonal, a sharp convex-order inequality for 1-Lipschitz functions, the conditional convex order, and a coupling construction based on conditional comonotonicity and the supermodular order. As a consequence, we obtain a normalized Wasserstein-based dependence measure that characterizes independence and attains its maximal value exactly for comonotone and countermonotone dependence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23940",
  "author_total": 1,
  "authors": [
    {
      "name": "Jonathan Ansari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55pgnyqc2mrqp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23940",
  "fulltext_url": null,
  "id": "55pgnyqc2mrqp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23940",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214045888",
  "pdf_url": "https://arxiv.org/pdf/2609.23940",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55pgnyqc2mrqp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23940",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23940"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Copulas farthest from independence in quadratic Wasserstein distance",
  "title_text": "Copulas farthest from independence in quadratic Wasserstein distance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/55pgnyqc2mrqp",
  "venue": "arXiv",
  "versions": []
}