Box-Covariances of Hyperuniform Point Processes

J. Jalowy, H. Stange, ArXiv:2506.13661 (2025).

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Jalowy, JonasLibreCat ; Stange, Hanna
Abstract
In this work, we present a complete characterization of the covariance structure of number statistics in boxes for hyperuniform point processes. Under a standard integrability assumption, the covariance depends solely on the overlap of the faces of the box. Beyond this assumption, a novel interpolating covariance structure emerges. This enables us to identify a limiting Gaussian 'coarse-grained' process, counting the number of points in large boxes as a function of the box position. Depending on the integrability assumption, this process may be continuous or discontinuous, e.g. in d=1 it is given by an increment process of a fractional Brownian motion.
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arXiv:2506.13661
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Jalowy J, Stange H. Box-Covariances of Hyperuniform Point Processes. arXiv:250613661. Published online 2025.
Jalowy, J., & Stange, H. (2025). Box-Covariances of Hyperuniform Point Processes. In arXiv:2506.13661.
@article{Jalowy_Stange_2025, title={Box-Covariances of Hyperuniform Point Processes}, journal={arXiv:2506.13661}, author={Jalowy, Jonas and Stange, Hanna}, year={2025} }
Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” ArXiv:2506.13661, 2025.
J. Jalowy and H. Stange, “Box-Covariances of Hyperuniform Point Processes,” arXiv:2506.13661. 2025.
Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” ArXiv:2506.13661, 2025.

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