{"ID":2829522,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.12257","arxiv_id":"2512.12257","title":"A complete characterization of maximal copulas with a given track section","abstract":"Bivariate copulas with prescribed diagonal section were first studied by Bertino. Their maximality was studied so far only from the point of view of upper bounds which brings quasi-copulas into the picture and limits the resulting set substantially. We propose to study maximality of these families in the order theoretic sense. A copula C with given diagonal section δ is called undominated if there is no copula C' {\\neq} C with the same diagonal section δ such that C {\\leq} C'. The main contribution of this paper is a new method that provides copulas of the kind. This method generates a much wider class that contains the known upper bounds as a very small subclass. There was a recent call for the study of asymmetry which is addressed by our class better than by the known ones. Corresponding quasi-copulas can be obtained from our copulas via splicing techniques. Most results are given on the level of tracks.","short_abstract":"Bivariate copulas with prescribed diagonal section were first studied by Bertino. Their maximality was studied so far only from the point of view of upper bounds which brings quasi-copulas into the picture and limits the resulting set substantially. We propose to study maximality of these families in the order theoreti...","url_abs":"https://arxiv.org/abs/2512.12257","url_pdf":"https://arxiv.org/pdf/2512.12257v1","authors":"[\"Matjaž Omladič\",\"Damjan Škulj\"]","published":"2025-12-13T09:44:05Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}