{
  "abstract": "Based on a new Kantorovich–Rubinstein duality principle for the Hessian that was recently established by the two authors, we extend the Rio inequality to any dimension $$d \\ge 1$$ d ≥ 1 with an optimal constant. Similarly, we propose an optimal upper bound for the ratio of Zolotarev distance $$Z_2(\\mu ,\\nu )$$ Z 2 ( μ , ν ) to Wasserstein distance $$W_2(\\mu ,\\nu )$$ W 2 ( μ , ν ) when $$\\mu ,\\nu \\in \\mathcal {P}_2(\\mathbb {R}^d)$$ μ , ν ∈ P 2 ( R d ) are centred probabilities with prescribed variances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Karol Bołbotowski"
    },
    {
      "name": "Guy Bouchitté"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2j4fvr8xbhg6d.bib",
  "cited_by": 0,
  "doi": "10.1007/s00440-026-01527-4",
  "fulltext_url": null,
  "id": "2j4fvr8xbhg6d",
  "issns": [
    "0178-8051",
    "1432-2064"
  ],
  "landing_url": "https://hal.science/hal-05846473v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7171812254",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00440-026-01527-4.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-30",
  "publisher": "Springer Verlag",
  "ris": "https://research.draconitic.com/paper/2j4fvr8xbhg6d.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:20:56Z",
      "native_id": "hal-05846473",
      "source": "hal",
      "url": "https://hal.science/hal-05846473v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Sharp inequalities between Zolotarev and Wasserstein distances in $$\\mathcal {P}_2(\\mathbb {R}^d)$$",
  "title_text": "Sharp inequalities between Zolotarev and Wasserstein distances in 𝒫_2(ℝ^d)",
  "type": "peer-reviewed",
  "updated_at": "2026-11-02T12:20:44Z",
  "url": "https://research.draconitic.com/paper/2j4fvr8xbhg6d",
  "venue": "Probability Theory and Related Fields",
  "versions": []
}