{
  "abstract": "Embedding subsets of Wasserstein spaces into linear spaces is a problem of both theoretical and computational interest. In this work, we prove that three classical and natural embeddings of Wasserstein spaces into Banach spaces of non-trivial type are bi-Hölder on subsets of Wasserstein spaces given by moment bounds. These embeddings, all considered in multiple applications, are the linearized optimal transport embedding, the sliced-Wasserstein embedding, and a particular kernel mean embedding. Our results contrast with known obstructions to embeddin the full Wasserstein space into Banach spaces of non-trivial type. We also show the sharpness of our results regarding the moments required for our conclusions to hold.",
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  "article_type": null,
  "arxiv": "2610.12029",
  "author_total": 2,
  "authors": [
    {
      "name": "Cyril Letrouit"
    },
    {
      "name": "Quentin Merigot"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/548fadw6r47k0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12029",
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  "id": "548fadw6r47k0",
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  "language": "en",
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  "pdf_url": "https://hal.science/hal-05788044/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/548fadw6r47k0.ris",
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    {
      "first_seen": "2026-10-30T12:17:52Z",
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      "native_id": "2610.12029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12029"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
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    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Embedding large subsets of Wasserstein spaces into Banach spaces",
  "title_text": "Embedding large subsets of Wasserstein spaces into Banach spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/548fadw6r47k0",
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