{
  "abstract": "We study the $p$-Bures-Wasserstein distance $D_p(A,B)=(\\mathrm{tr}\\,A^p+\\mathrm{tr}\\,B^p-2\\|A^{1/2}B^{1/2}\\|_p^p)^{1/2}$ on positive semidefinite matrices; it equals the Bures-Wasserstein distance for $p=1$, and the Hilbert-Schmidt distance for $p=2$. We prove that $D_p$ is a metric for every $1\\le p\\le2$, by proving a stronger 2014 conjecture of Lin and van den Driessche on $3\\times3$ block matrices. Our main tool is a partition inequality for Schatten norms, proved by complex interpolation. We also characterize Fréchet means for $D_p$ by a fixed-point equation and prove geometric convergence of the associated iteration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15889",
  "author_total": 1,
  "authors": [
    {
      "name": "Suvrit Sra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/36t7nrv5erev7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15889",
  "fulltext_url": null,
  "id": "36t7nrv5erev7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15889",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7221771628",
  "pdf_url": "https://arxiv.org/pdf/2610.15889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/36t7nrv5erev7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The $p$-Bures-Wasserstein distance via $3\\times3$ block matrices (with application to $p$-Bures-Wasserstein barycenters)",
  "title_text": "The p-Bures-Wasserstein distance via 3×3 block matrices (with application to p-Bures-Wasserstein barycenters)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/36t7nrv5erev7",
  "venue": "arXiv",
  "versions": []
}