Random complex zeroes, I. Asymptotic normality

Abstract

We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of zeroes.

26 pages. Version 2 (final): the end of the proof corrected (sections 3.2, 3.3); small insertions to Introduction and References