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  "slug": "gaussian-entropic-support-geometry",
  "title": "Support geometry and nonuniform small-entropy limits in Gaussian transport",
  "shortTitle": "When small entropy is not small enough",
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  "oneLine": "Support angles govern Gaussian joint-plan sensitivity: exact singular-support coefficients and a uniform remainder with explicit gap conditions.",
  "abstract": "How much does adding entropy change a Gaussian transport plan? This unrefereed candidate derives the small-entropy coefficient on arbitrary supports, its sharp support-dependent bound, and explicit angle-conditioned remainder control. A moving positive-definite family shows that bounded total variance alone does not yield uniform convergence. The known full-rank coefficient is credited to public MathDB proofs.",
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    "Gaussian optimal transport",
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    {
      "citation": "Akyildiz, Del Moral and Miguez (2025), Gaussian entropic optimal transport: Schrödinger bridges and the Sinkhorn algorithm. Version 5.",
      "url": "https://arxiv.org/html/2412.18432v5",
      "doi": null
    },
    {
      "citation": "Patel, The sharp universal constant is d/2. Public MathDB submission; platform unverified, exact posting timestamp not independently authenticated.",
      "url": "https://mathdb.com/p/372212/universal-bound-conjecture-for-gaussian-entropic-optimal-tra",
      "doi": null
    },
    {
      "citation": "principia math, The sharp universal Gaussian EOT coupling bound. Public MathDB submission; platform status is not external verification.",
      "url": "https://mathdb.com/p/372212/universal-bound-conjecture-for-gaussian-entropic-optimal-tra",
      "doi": null
    },
    {
      "citation": "Freulon, Georgakis and Panaretos (2026), Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean space. Version 2.",
      "url": "https://arxiv.org/html/2507.01709v2",
      "doi": null
    },
    {
      "citation": "Janati, Muzellec, Peyré and Cuturi (2020), Entropic Optimal Transport between Unbalanced Gaussian Measures has a Closed Form. NeurIPS 2020.",
      "url": "https://doi.org/10.48550/arXiv.2006.02572",
      "doi": "10.48550/arXiv.2006.02572"
    },
    {
      "citation": "Minh (2022), Entropic regularization of Wasserstein distance between infinite-dimensional Gaussian measures and Gaussian processes. Version 3.",
      "url": "https://arxiv.org/html/2011.07489v3",
      "doi": null
    },
    {
      "citation": "Mallasto, Gerolin and Minh (2022), Entropy-regularized 2-Wasserstein distance between Gaussian measures. Information Geometry.",
      "url": "https://doi.org/10.1007/s41884-021-00052-8",
      "doi": "10.1007/s41884-021-00052-8"
    },
    {
      "citation": "Yun (2026), Spectral Shrinkage of Gaussian Entropic Optimal Transport. Version 2.",
      "url": "https://arxiv.org/html/2512.19457v2",
      "doi": null
    },
    {
      "citation": "Bhatia and Kittaneh (1990), On the singular values of a product of operators. SIAM Journal on Matrix Analysis and Applications.",
      "url": "https://doi.org/10.1137/0611018",
      "doi": "10.1137/0611018"
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