Probabilistic frames and Wasserstein distances
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911007635406848 |
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| author | Chen, Dongwei Schmoll, Martin |
| author_facet | Chen, Dongwei Schmoll, Martin |
| contents | We use Wasserstein distances to characterize and study probabilistic frames. Adapting results from Olkin and Pukelsheim, from Gelbrich and from Cuesta-Albertos, Matran-Bea and Tuero-Diaz to frame operators, we show that the sets of probabilistic frames with given frame operator are homeomorphic by an optimal linear push-forward. Using the Wasserstein distances, we generalize several recent results in probabilistic frame theory and show path connectedness of the set of probabilistic frames with a fixed frame operator. We also describe transport duals that do not arise as push-forwards and characterize those that are push-forwards. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probabilistic frames and Wasserstein distances Chen, Dongwei Schmoll, Martin Probability Classical Analysis and ODEs 60A10, 42C15, 49Q22 We use Wasserstein distances to characterize and study probabilistic frames. Adapting results from Olkin and Pukelsheim, from Gelbrich and from Cuesta-Albertos, Matran-Bea and Tuero-Diaz to frame operators, we show that the sets of probabilistic frames with given frame operator are homeomorphic by an optimal linear push-forward. Using the Wasserstein distances, we generalize several recent results in probabilistic frame theory and show path connectedness of the set of probabilistic frames with a fixed frame operator. We also describe transport duals that do not arise as push-forwards and characterize those that are push-forwards. |
| title | Probabilistic frames and Wasserstein distances |
| topic | Probability Classical Analysis and ODEs 60A10, 42C15, 49Q22 |
| url | https://arxiv.org/abs/2501.02602 |