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

Raphael Butez; Sandrine Dallaporta; David García-Zelada

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arXiv · 2404.09549

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

Raphael Butez·Sandrine Dallaporta·David García-Zelada

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Abstract

We study the existence of bounds on the expected $p$-Wasserstein distance between a random measure and its mean under the assumption that the $p$-th centered moments of the counting statistics are controlled uniformly in space. The average Wasserstein transport cost is shown to be bounded from above and from below by some multiples of the number of points. $D$-dimensional versions of those results are also obtained. As a corollary, we prove that for any value of $p\geq 1$ the Ginibre point process can be seen as a perturbed lattice with identically distributed perturbations with a finite $p$-th moment.

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Raphael Butez, Sandrine Dallaporta, David García-Zelada. 2024-04-15. On the Wasserstein distance between a hyperuniform point process and its mean. https://arxiv.org/abs/2404.09549

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