Asymptotic Mass Distribution of Random Holomorphic Sections
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909974103326720 |
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| author | Bayraktar, Turgay Bojnik, Afrim |
| author_facet | Bayraktar, Turgay Bojnik, Afrim |
| contents | In this note, we prove a central limit theorem for the mass distribution of random holomorphic sections associated with a sequence of positive line bundles endowed with $\mathscr{C}^3$ Hermitian metrics over a compact Kähler manifold. In addition, we show that almost every sequence of such random holomorphic sections exhibits quantum ergodicity in the sense of Zelditch. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07120 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Mass Distribution of Random Holomorphic Sections Bayraktar, Turgay Bojnik, Afrim Complex Variables Differential Geometry Probability In this note, we prove a central limit theorem for the mass distribution of random holomorphic sections associated with a sequence of positive line bundles endowed with $\mathscr{C}^3$ Hermitian metrics over a compact Kähler manifold. In addition, we show that almost every sequence of such random holomorphic sections exhibits quantum ergodicity in the sense of Zelditch. |
| title | Asymptotic Mass Distribution of Random Holomorphic Sections |
| topic | Complex Variables Differential Geometry Probability |
| url | https://arxiv.org/abs/2505.07120 |