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Pré-Publication, Document De Travail Année : 2024

On the Wasserstein distance between a hyperuniform point process and its mean

Résumé

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.
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Dates et versions

hal-04544006 , version 1 (12-04-2024)
hal-04544006 , version 2 (19-07-2024)

Identifiants

  • HAL Id : hal-04544006 , version 1

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Raphael Butez, Sandrine Dallaporta, David García-Zelada. On the Wasserstein distance between a hyperuniform point process and its mean. 2024. ⟨hal-04544006v1⟩
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