Zeros of Gaussian Analytic Functions

Details Zeros of Gaussian Analytic Functions Zeros of Gaussian Analytic Functions

2000-07-06

arxiv.org/abs/math/0007030v1

Mathematics

Complex Variables

14 pages, to be published in Math. Res. Lett

Scientific paper

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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