Box-Covariances of Hyperuniform Point Processes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911714769895424 |
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| author | Jalowy, Jonas Stange, Hanna |
| author_facet | Jalowy, Jonas Stange, Hanna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Box-Covariances of Hyperuniform Point Processes Jalowy, Jonas Stange, Hanna Probability Primary: 60G55, Secondary: 60F05, 60G50 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. |
| title | Box-Covariances of Hyperuniform Point Processes |
| topic | Probability Primary: 60G55, Secondary: 60F05, 60G50 |
| url | https://arxiv.org/abs/2506.13661 |