Zeros of Gaussian Analytic Functions
Complex Variables
2007-05-23 v1 Probability
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.
Keywords
Cite
@article{arxiv.math/0007030,
title = {Zeros of Gaussian Analytic Functions},
author = {Mikhail Sodin},
journal= {arXiv preprint arXiv:math/0007030},
year = {2007}
}
Comments
14 pages, to be published in Math. Res. Lett