Rigid and flexible Wasserstein spaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912653184598016 |
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| author | Balogh, Zoltán M. Ströher, Eric Titkos, Tamás Virosztek, Dániel |
| author_facet | Balogh, Zoltán M. Ströher, Eric Titkos, Tamás Virosztek, Dániel |
| contents | In this paper, we study isometries of $p$-Wasserstein spaces. In our first result, for every complete and separable metric space $X$ and for every $p\geq1$, we construct a metric space $Y$ such that $X$ embeds isometrically into $Y$, and the $p$-Wasserstein space over $Y$ admits mass-splitting isometries. Our second result is about embeddings into rigid constructions. We show that any complete and separable metric space $X$ can be embedded isometrically into a metric space $Y$ such that the $1$-Wasserstein space is isometrically rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigid and flexible Wasserstein spaces Balogh, Zoltán M. Ströher, Eric Titkos, Tamás Virosztek, Dániel Metric Geometry Functional Analysis Probability 46E27, 49Q22, 54E40 In this paper, we study isometries of $p$-Wasserstein spaces. In our first result, for every complete and separable metric space $X$ and for every $p\geq1$, we construct a metric space $Y$ such that $X$ embeds isometrically into $Y$, and the $p$-Wasserstein space over $Y$ admits mass-splitting isometries. Our second result is about embeddings into rigid constructions. We show that any complete and separable metric space $X$ can be embedded isometrically into a metric space $Y$ such that the $1$-Wasserstein space is isometrically rigid. |
| title | Rigid and flexible Wasserstein spaces |
| topic | Metric Geometry Functional Analysis Probability 46E27, 49Q22, 54E40 |
| url | https://arxiv.org/abs/2502.09364 |