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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.19514 |
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| _version_ | 1866915276692389888 |
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| author | Hammarhjelm, Gustav Strömbergsson, Andreas Yu, Shucheng |
| author_facet | Hammarhjelm, Gustav Strömbergsson, Andreas Yu, Shucheng |
| contents | For quasicrystals of cut-and-project type in $\mathbb{R}^d$, it was proved by Marklof and Strömbergsson that the limit local statistical properties of the directions to the points in the set are described by certain $\operatorname{SL}_d(\mathbb{R})$-invariant point processes. In the present paper we make a detailed study of the tail asymptotics of the limiting gap statistics of the directions, for certain specific classes of planar quasicrystals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic estimates of large gaps between directions in certain planar quasicrystals Hammarhjelm, Gustav Strömbergsson, Andreas Yu, Shucheng Number Theory Mathematical Physics Dynamical Systems Probability For quasicrystals of cut-and-project type in $\mathbb{R}^d$, it was proved by Marklof and Strömbergsson that the limit local statistical properties of the directions to the points in the set are described by certain $\operatorname{SL}_d(\mathbb{R})$-invariant point processes. In the present paper we make a detailed study of the tail asymptotics of the limiting gap statistics of the directions, for certain specific classes of planar quasicrystals. |
| title | Asymptotic estimates of large gaps between directions in certain planar quasicrystals |
| topic | Number Theory Mathematical Physics Dynamical Systems Probability |
| url | https://arxiv.org/abs/2409.19514 |