Number rigid determinantal point processes induced by generalized Cantor sets
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910535111409664 |
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| author | Lin, Zhaofeng Qiu, Yanqi Wang, Kai |
| author_facet | Lin, Zhaofeng Qiu, Yanqi Wang, Kai |
| contents | We consider the Ghosh-Peres number rigidity of translation-invariant determinantal point processes on the real line $\mathbb{R}$, whose correlation kernels are induced by the Fourier transform of the indicators of generalized Cantor sets in the unit interval. Our main results show that for any given $θ\in(0,1)$, there exists a generalized Cantor set with Lebesgue measure $θ$, such that the corresponding determinantal point process is Ghosh-Peres number rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Number rigid determinantal point processes induced by generalized Cantor sets Lin, Zhaofeng Qiu, Yanqi Wang, Kai Probability We consider the Ghosh-Peres number rigidity of translation-invariant determinantal point processes on the real line $\mathbb{R}$, whose correlation kernels are induced by the Fourier transform of the indicators of generalized Cantor sets in the unit interval. Our main results show that for any given $θ\in(0,1)$, there exists a generalized Cantor set with Lebesgue measure $θ$, such that the corresponding determinantal point process is Ghosh-Peres number rigid. |
| title | Number rigid determinantal point processes induced by generalized Cantor sets |
| topic | Probability |
| url | https://arxiv.org/abs/2407.14168 |