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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2511.10610 |
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| _version_ | 1866911263902138368 |
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| author | Djellouli, Youssef Lamarre, Pierre Yves Gaudreau |
| author_facet | Djellouli, Youssef Lamarre, Pierre Yves Gaudreau |
| contents | We study the occurrence of number rigidity and deletion singularity in a class of point processes that we call {\it projected perturbed lattices}. These are generalizations of processes of the form $Π=\{\|z\|^α+g_z\}_{z\in\mathbb{Z}^d}$ where $(g_z)_{z\in\mathbb{Z}^d}$ are jointly Gaussian, $α>0$, $d\in\mathbb{N}$, and $\|\cdot\|$ is a norm. We develop a new technique to prove sufficient conditions for the deletion singularity of $Π$, which improves significantly on the conditions one can obtain using the standard rigidity toolkit (e.g., the variance of linear statistics). In particular, we obtain the first lower bounds on $α$ for the deletion singularity of $Π$ that are independent of the dimension $d$ and the correlation of the $g_z$'s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Rigidity of Projected Perturbed Lattices Djellouli, Youssef Lamarre, Pierre Yves Gaudreau Probability We study the occurrence of number rigidity and deletion singularity in a class of point processes that we call {\it projected perturbed lattices}. These are generalizations of processes of the form $Π=\{\|z\|^α+g_z\}_{z\in\mathbb{Z}^d}$ where $(g_z)_{z\in\mathbb{Z}^d}$ are jointly Gaussian, $α>0$, $d\in\mathbb{N}$, and $\|\cdot\|$ is a norm. We develop a new technique to prove sufficient conditions for the deletion singularity of $Π$, which improves significantly on the conditions one can obtain using the standard rigidity toolkit (e.g., the variance of linear statistics). In particular, we obtain the first lower bounds on $α$ for the deletion singularity of $Π$ that are independent of the dimension $d$ and the correlation of the $g_z$'s. |
| title | On the Rigidity of Projected Perturbed Lattices |
| topic | Probability |
| url | https://arxiv.org/abs/2511.10610 |