A GEOMETRIC STUDY OF WASSERSTEIN SPACES: ULTRAMETRICS

DOI10.1112/S0025579314000059zbMath1312.30069arXiv1304.5219MaRDI QIDQ5179258

Benoît R. Kloeckner

Publication date: 19 March 2015

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.5219

zbMATH Keywords

Wasserstein distancespace of measurescompact ultrametric space

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Geometric embeddings of metric spaces (30L05)

Related Items (11)

On emergence and complexity of ergodic decompositions ⋮ Randomized Wasserstein Barycenter Computation: Resampling with Statistical Guarantees ⋮ Unnamed Item ⋮ Kantorovich distance on finite metric spaces: Arens-Eells norm and CUT norms ⋮ Tropical optimal transport and Wasserstein distances ⋮ Isometric rigidity of Wasserstein tori and spheres ⋮ Wasserstein distance and metric trees ⋮ The ultrametric Gromov-Wasserstein distance ⋮ Isometric study of Wasserstein spaces – the real line ⋮ Free spaces over some proper metric spaces ⋮ Kantorovich-Rubinstein distance and barycenter for finitely supported measures: foundations and algorithms

Cites Work

• A convexity principle for interacting gases
• An introduction to the Ribe program
• Ultrametric subsets with large Hausdorff dimension
• A GENERALIZATION OF HAUSDORFF DIMENSION APPLIED TO HILBERT CUBES AND WASSERSTEIN SPACES
• A GEOMETRIC STUDY OF WASSERSTEIN SPACES: HADAMARD SPACES
• Ultrametric skeletons
• Optimal Transport

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