A geometric study of Wasserstein spaces: Euclidean spaces

By Benoît R. Kloeckner. 2008

82 citations recorded by the source corpus.

We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of the line, there exists a (unique) ``exotic'' isometric flow. This contrasts with the case of higher-dimensional Euclidean spaces, where all isometries of the Wasserstein space preserve the shape of measures. We also study the curvature and various ranks of these spaces.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d528aadbdff6b24218b1f158ca414703d0f13b14

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In Applied Mathematics

1. Yaqing Chen
2. H. Muller
3. Zhenhua Lin
4. Victor M. Panaretos
5. Laya Ghodrati
6. Kengo Kato

In Astronomy and Astrophysics

1. H. Muller

In Mathematical Physics

1. Yaqing Chen
2. H. Muller
3. Zhenhua Lin

Citations in the corpus

• Wasserstein Regression (2020, background): “Since the Wasserstein spaceW is a Hadamard space (Kloeckner 2010), there exists a unique minimizer of EdW (·, ν1) (Sturm 2003), i.”