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Zeros of Gaussian Analytic Functions

Mikhail Sodin
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Abstract

We prove and discuss three results on zero distribution of gaussian analytic functions: (i) the Edeleman-Kostlan formula for the expectation of the counting measure; (ii) a variation on the theme of Calabi's rigidity theorem; (iii) Offord's estimate of exponential decay of the tail probabilities of an anlytic function having an access or deficiency of zeros in a given region.

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Mikhail Sodin. 2000-07-06. Zeros of Gaussian Analytic Functions. https://arxiv.org/abs/math/0007030

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