Wasserstein geometry and Ricci curvature bounds for Poisson spaces (Q6603926)
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scientific article; zbMATH DE number 7912281
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wasserstein geometry and Ricci curvature bounds for Poisson spaces |
scientific article; zbMATH DE number 7912281 |
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Wasserstein geometry and Ricci curvature bounds for Poisson spaces (English)
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12 September 2024
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The authors construct a Riemannian structure on the space of Poisson point processes, where the intrinsic distance \(W\) corresponds to the Benamou-Brenier variational formula, the closure of the domain of the relative entropy is a complete geodesic space, and the Ricci curvature is bounded below by \(1\). Moreover, the Ornstein-Uhlenbeck semigroup is associated with the gradient flow of the relative entropy, and the HWI inequality holds true.
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Poisson point process
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optimal transportation
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Wasserstein distance
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gradient flows
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Ricci curvature
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