Accumulated spectrograms for hyperuniform determinantal point processes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911819964088320 |
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| author | Katori, Makoto Lazag, Pierre Shirai, Tomoyuki |
| author_facet | Katori, Makoto Lazag, Pierre Shirai, Tomoyuki |
| contents | We define the accumulated spectrogram associated to a locally trace class orthogonal projection operator and to a bounded set using the polar decomposition of its restriction on that set and prove a convergence theorem for accumulated spectrograms along an exhaustion in the case when the corresponding determinantal point process is hyperuniform. We prove that a radial determinantal point process on Rd is always hyperuniform along the exhaustion formed by the dilations of a bounded open set, and as a consequence, we obtain that dilations of the corresponding accumulated spectrogram converge to the indicator function of the considered set, establishing thus a universal phenomenon. Our result is a generalisation of a theorem by Abreu-Gröchenig-Romero in [1] concerning time-frequency localization operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accumulated spectrograms for hyperuniform determinantal point processes Katori, Makoto Lazag, Pierre Shirai, Tomoyuki Probability Mathematical Physics Classical Analysis and ODEs Functional Analysis We define the accumulated spectrogram associated to a locally trace class orthogonal projection operator and to a bounded set using the polar decomposition of its restriction on that set and prove a convergence theorem for accumulated spectrograms along an exhaustion in the case when the corresponding determinantal point process is hyperuniform. We prove that a radial determinantal point process on Rd is always hyperuniform along the exhaustion formed by the dilations of a bounded open set, and as a consequence, we obtain that dilations of the corresponding accumulated spectrogram converge to the indicator function of the considered set, establishing thus a universal phenomenon. Our result is a generalisation of a theorem by Abreu-Gröchenig-Romero in [1] concerning time-frequency localization operators. |
| title | Accumulated spectrograms for hyperuniform determinantal point processes |
| topic | Probability Mathematical Physics Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2403.16325 |