Hyperuniformity of self-similar point processes
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918534689325056 |
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| author | Roca, Daniel |
| author_facet | Roca, Daniel |
| contents | We study hyperuniformity of self-similar point processes arising from substitution rules in two dimensions. In particular, we derive a sufficient condition for hyperuniformity of these point processes only in terms of the associated substitution matrix. This condition applies to a wide class of examples for which hyperuniformity had not yet been established, including most well-known examples of planar self-similar tilings. In particular, we show that the Godrèche-Lançon-Billard substitution rule gives rise to hyperuniform point processes with singular continuous diffraction. Furthermore, we prove that hyperuniformity is not an MLD invariant, contradicting standing conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20517 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperuniformity of self-similar point processes Roca, Daniel Dynamical Systems Probability We study hyperuniformity of self-similar point processes arising from substitution rules in two dimensions. In particular, we derive a sufficient condition for hyperuniformity of these point processes only in terms of the associated substitution matrix. This condition applies to a wide class of examples for which hyperuniformity had not yet been established, including most well-known examples of planar self-similar tilings. In particular, we show that the Godrèche-Lançon-Billard substitution rule gives rise to hyperuniform point processes with singular continuous diffraction. Furthermore, we prove that hyperuniformity is not an MLD invariant, contradicting standing conjectures. |
| title | Hyperuniformity of self-similar point processes |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2310.20517 |