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Universality results for zeros of random holomorphic sections

Bayraktar, Turgay and Coman, Dan and Marinescu, George (2020) Universality results for zeros of random holomorphic sections. Transactions of the American Mathematical Society, 373 (6). pp. 3765-3791. ISSN 0002-9947 (Print) 1088-6850 (Online)

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Abstract

In this work we prove an universality result regarding the equidistribution of zeros of random holomorphic sections associated to a sequence of singular Hermitian holomorphic line bundles on a compact Kahler complex space X. Namely, under mild moment assumptions, we show that the asymptotic distribution of zeros of random holomorphic sections is independent of the choice of the probability measure on the space of holomorphic sections. In the case when X is a compact Kahler manifold, we also prove an off-diagonal exponential decay estimate for the Bergman kernels of a sequence of positive line bundles on X.
Item Type: Article
Subjects: Q Science > QA Mathematics > QA299.6-433 Analysis
Q Science > QA Mathematics > QA440 Geometry. Trigonometry. Topology
Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Turgay Bayraktar
Date Deposited: 08 Jun 2020 15:35
Last Modified: 31 Jul 2023 17:02
URI: https://research.sabanciuniv.edu/id/eprint/39922

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