A central limit theorem associated with a sequence of positive line bundles

Afrim Bojnik; Ozan Günyüz

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arXiv · 2405.03479

A central limit theorem associated with a sequence of positive line bundles

Afrim Bojnik·Ozan Günyüz

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Abstract

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 K\"{a}hler 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.

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Afrim Bojnik, Ozan Günyüz. 2024-05-06. A central limit theorem associated with a sequence of positive line bundles. https://arxiv.org/abs/2405.03479

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