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Universality results for zeros of random holomorphic sections

By Turgay Bayraktar, Dan Coman and George Marinescu

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

Topics: QA299.6-433 Analysis, QA440 Geometry. Trigonometry. Topology, QA273-280 Probabilities. Mathematical statistics
Publisher: 'American Mathematical Society (AMS)'
Year: 2020
DOI identifier: 10.1090/tran/7807
OAI identifier: oai:research.sabanciuniv.edu:39922

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