Zeros of Gaussian Analytic Functions

2000/07/06 by Mikhail Sodin, Sodin, Mikhail · 2 citations
Mathematics · #30B20 #Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR) #math.CV #math.PR #msc:30B20

paper · pdf · doi:10.48550/arxiv.math/0007030

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

arxiv created 2000/07/06 · arxiv updated 2009/11/30

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.

Cited by

• Local repulsion between zeros and critical points of the Gaussian Entire Function
• Sampling properties of the zeroes of the Gaussian entire function

Related

• Zeroes of Gaussian analytic functions
• Zeros and coefficients
• Zeros of Random Analytic Functions
• On Gaussians, Zeros, and Linear Combinations of L-functions. Part A: Entire Functions of Beurling-Selberg Type and Probability Distributions
• Overcrowding for zeros of Hyperbolic Gaussian analytic functions