{
  "abstract": "In [H. Lavenant, J. Luckhardt, G. Mordant, B. Schmitzer, L. Tamanini, The Riemannian geometry of Sinkhorn divergences. Ann. Inst. H. Poincaré Anal. Non Linéaire 43 (2026)] we introduced a Riemannian metric $\\mathsf{d}_S$ on the space of probability distributions obtained from entropic optimal transport, specifically from the Sinkhorn divergence $S_\\varepsilon$. In the present work we discuss how to approximate and compute $\\mathsf{d}_S$. Spatially, we prove Gromov--Hausdorff convergence of the metric and convergence of geodesics for increasingly fine Eulerian discretization of the base space. Temporally, we show $Γ$-convergence of the chain discretization $N \\sum_{k=0}^{N-1} S_\\varepsilon(μ_k, μ_{k+1})$ to the energy functional defining $\\mathsf{d}_S$. We deduce and implement numerical schemes to compute approximations of $\\mathsf{d}_S$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02007",
  "author_total": 3,
  "authors": [
    {
      "name": "Hugo Lavenant"
    },
    {
      "name": "Jonas Luckhardt"
    },
    {
      "name": "Bernhard Schmitzer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/btgak55mpcyzd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02007",
  "fulltext_url": null,
  "id": "btgak55mpcyzd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02007",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7216086300",
  "pdf_url": "https://arxiv.org/pdf/2610.02007",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/btgak55mpcyzd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02007",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02007"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Approximation and computation of the geodesic Sinkhorn distance",
  "title_text": "Approximation and computation of the geodesic Sinkhorn distance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/btgak55mpcyzd",
  "venue": "arXiv",
  "versions": []
}