(Non)-hyperuniformity of perturbed lattices
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915378375950336 |
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| author | Dereudre, David Flimmel, Daniela Huesmann, Martin Leblé, Thomas |
| author_facet | Dereudre, David Flimmel, Daniela Huesmann, Martin Leblé, Thomas |
| contents | We ask whether a stationary lattice in dimension $d$ whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When $d = 1$ or $2$, we show that it is the case when the perturbations have a finite $d$-moment, and that this condition is sharp. When $d \geq 3$, we construct arbitrarily small perturbations such that the resulting point process is not hyperuniform. As a side remark of independent interest, we exhibit hyperuniform processes with arbitrarily slow decay of their number variance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | (Non)-hyperuniformity of perturbed lattices Dereudre, David Flimmel, Daniela Huesmann, Martin Leblé, Thomas Probability We ask whether a stationary lattice in dimension $d$ whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When $d = 1$ or $2$, we show that it is the case when the perturbations have a finite $d$-moment, and that this condition is sharp. When $d \geq 3$, we construct arbitrarily small perturbations such that the resulting point process is not hyperuniform. As a side remark of independent interest, we exhibit hyperuniform processes with arbitrarily slow decay of their number variance. |
| title | (Non)-hyperuniformity of perturbed lattices |
| topic | Probability |
| url | https://arxiv.org/abs/2405.19881 |