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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2311.13441 |
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| _version_ | 1866909286362251264 |
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| author | de Reyna, Juan Arias Rodgers, Brad |
| author_facet | de Reyna, Juan Arias Rodgers, Brad |
| contents | This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting point process are equivalent. In particular we consider convergence in correlation, convergence in distribution, and convergence of spacings between points. We also prove a simple Tauberian theorem regarding rescaled correlations. The results are applied to zeros of the Riemann zeta-function to show that several ways to state the GUE Hypothesis are equivalent. The proof relies on a moment bound of A. Fujii. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13441 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On convergence of points to limiting processes, with an application to zeta zeros de Reyna, Juan Arias Rodgers, Brad Number Theory Probability This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting point process are equivalent. In particular we consider convergence in correlation, convergence in distribution, and convergence of spacings between points. We also prove a simple Tauberian theorem regarding rescaled correlations. The results are applied to zeros of the Riemann zeta-function to show that several ways to state the GUE Hypothesis are equivalent. The proof relies on a moment bound of A. Fujii. |
| title | On convergence of points to limiting processes, with an application to zeta zeros |
| topic | Number Theory Probability |
| url | https://arxiv.org/abs/2311.13441 |