A central limit theorem associated with a sequence of positive line bundles
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916601730695168 |
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| author | Bojnik, Afrim Günyüz, Ozan |
| author_facet | Bojnik, Afrim Günyüz, Ozan |
| contents | We prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact Kähler manifold. In the course of our analysis, we derive first-order asymptotics and upper decay estimates for near and off-diagonal Bergman kernels, respectively. These results are essential for determining the statistical properties of the zeros of random holomorphic sections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A central limit theorem associated with a sequence of positive line bundles Bojnik, Afrim Günyüz, Ozan Complex Variables Differential Geometry Probability We prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact Kähler manifold. In the course of our analysis, we derive first-order asymptotics and upper decay estimates for near and off-diagonal Bergman kernels, respectively. These results are essential for determining the statistical properties of the zeros of random holomorphic sections. |
| title | A central limit theorem associated with a sequence of positive line bundles |
| topic | Complex Variables Differential Geometry Probability |
| url | https://arxiv.org/abs/2405.03479 |