{
  "abstract": "We prove quantitative stability of quadratic optimal transport maps from arbitrary log-concave sources to bounded targets. If the source $ρ$ is isotropic on $\\mathbb R^d$ and the targets $μ$, $ν$ are supported in a common ball of radius $R$, their Brenier maps satisfy \\[ \\lVert T_μ-T_ν\\rVert_{L^2(ρ)} \\leqslant 17d^{2/3}R^{2/3}W_2(μ,ν)^{1/3}. \\] The one-third exponent is optimal for $d\\geqslant2$. The proof combines a linear stability estimate for Brenier potentials in a weighted norm with a matching weighted reverse Poincaré inequality. The weight is chosen in terms of the negative log-density of the source to account for its tails. We also show that the best dimensional constant in map stability is at least of order $d^{1/3}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05534",
  "author_total": 2,
  "authors": [
    {
      "name": "Songbo Wang"
    },
    {
      "name": "Xiaozhen Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejnbqc9f3tdce.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05534",
  "fulltext_url": null,
  "id": "ejnbqc9f3tdce",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05534",
  "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.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05534",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejnbqc9f3tdce.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05534",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05534"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "One-third Hölder stability of optimal transport maps from log-concave sources",
  "title_text": "One-third Hölder stability of optimal transport maps from log-concave sources",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/ejnbqc9f3tdce",
  "venue": "arXiv",
  "versions": []
}