On the Wasserstein distance between a hyperuniform point process and its mean
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909262717911040 |
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| author | Butez, Raphael Dallaporta, Sandrine García-Zelada, David |
| author_facet | Butez, Raphael Dallaporta, Sandrine García-Zelada, David |
| contents | We study the average $p-$Wasserstein distance between a finite sample of an infinite hyperuniform point process on $\mathbb{R}^2$ and its mean for any $p\geq 1$. The average Wasserstein transport cost is shown to be bounded from above and from below by some multiples of the number of points. More generally, we give a control on the $p-$Wasserstein distance in function of a control on the $L^p$ norm of the difference of the point process and its mean. We also obtain the $d$-dimensional version of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Wasserstein distance between a hyperuniform point process and its mean Butez, Raphael Dallaporta, Sandrine García-Zelada, David Probability We study the average $p-$Wasserstein distance between a finite sample of an infinite hyperuniform point process on $\mathbb{R}^2$ and its mean for any $p\geq 1$. The average Wasserstein transport cost is shown to be bounded from above and from below by some multiples of the number of points. More generally, we give a control on the $p-$Wasserstein distance in function of a control on the $L^p$ norm of the difference of the point process and its mean. We also obtain the $d$-dimensional version of this result. |
| title | On the Wasserstein distance between a hyperuniform point process and its mean |
| topic | Probability |
| url | https://arxiv.org/abs/2404.09549 |