{"abstract":[{"lang":"eng","text":"In this work, we present a complete characterization of the covariance\r\nstructure of number statistics in boxes for hyperuniform point processes. Under\r\na standard integrability assumption, the covariance depends solely on the\r\noverlap of the faces of the box. Beyond this assumption, a novel interpolating\r\ncovariance structure emerges. This enables us to identify a limiting Gaussian\r\n'coarse-grained' process, counting the number of points in large boxes as a\r\nfunction of the box position. Depending on the integrability assumption, this\r\nprocess may be continuous or discontinuous, e.g. in d=1 it is given by an\r\nincrement process of a fractional Brownian motion."}],"date_created":"2025-06-22T08:02:28Z","status":"public","external_id":{"arxiv":["2506.13661"]},"publication":"arXiv:2506.13661","date_updated":"2025-06-22T08:03:20Z","citation":{"ieee":"J. Jalowy and H. Stange, “Box-Covariances of Hyperuniform Point Processes,” <i>arXiv:2506.13661</i>. 2025.","apa":"Jalowy, J., &#38; Stange, H. (2025). Box-Covariances of Hyperuniform Point Processes. In <i>arXiv:2506.13661</i>.","chicago":"Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” <i>ArXiv:2506.13661</i>, 2025.","ama":"Jalowy J, Stange H. Box-Covariances of Hyperuniform Point Processes. <i>arXiv:250613661</i>. Published online 2025.","short":"J. Jalowy, H. Stange, ArXiv:2506.13661 (2025).","mla":"Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.” <i>ArXiv:2506.13661</i>, 2025.","bibtex":"@article{Jalowy_Stange_2025, title={Box-Covariances of Hyperuniform Point Processes}, journal={arXiv:2506.13661}, author={Jalowy, Jonas and Stange, Hanna}, year={2025} }"},"type":"preprint","language":[{"iso":"eng"}],"_id":"60293","title":"Box-Covariances of Hyperuniform Point Processes","year":"2025","user_id":"113768","department":[{"_id":"94"}],"author":[{"first_name":"Jonas","id":"113768","orcid":"0000-0001-9624-2685","last_name":"Jalowy","full_name":"Jalowy, Jonas"},{"first_name":"Hanna","last_name":"Stange","full_name":"Stange, Hanna"}]}