{
  "abstract": "We study functional inequalities along Wasserstein geodesics. If µ 0 and µ 1 are respectively κ 0 -and κ 1 -strongly log-concave probability measures on R n , we prove that their quadratic Wasserstein geodesic satisfies\n\nfor all probability measures ν on R n . The coefficient is sharp. By linearization, this recovers the Poincaré estimate of Han and Zhu [15]. On the real line, we prove convexity of the square roots of the optimal T 1 and T 2 constants along monotone interpolation between arbitrary probability measures. The argument applies to more general transport entropy inequalities. We also establish convexity of the rescaled L p Poincaré constants for every finite p ≥ 1, including the square root of the Poincaré constant and the inverse Cheeger constant. Finally, we construct a planar Wasserstein geodesic whose endpoints satisfy T 2 and all finite-p L p -Poincaré inequalities, whereas every interior interpolant fails these inequalities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39252",
  "author_total": 3,
  "authors": [
    {
      "name": "Nathael Gozlan"
    },
    {
      "name": "Hugo Malamut"
    },
    {
      "name": "Irène Waldspurger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aeh8qzpgrxbzq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39252",
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  "id": "aeh8qzpgrxbzq",
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  "landing_url": "https://hal.science/hal-05769896v1",
  "language": "en",
  "licence": "CC-BY-4.0",
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  "metadata_licence": "CC0-1.0",
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  "pdf_url": "https://hal.science/hal-05769896/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aeh8qzpgrxbzq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769896",
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      "url": "https://hal.science/hal-05769896v1"
    },
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39252"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Functional inequalities along Wasserstein geodesics",
  "title_text": "Functional inequalities along Wasserstein geodesics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/aeh8qzpgrxbzq",
  "venue": "HAL",
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}