Random complex zeroes, I. Asymptotic normality
Complex Variables
2007-05-23 v2 Mathematical Physics
math.MP
Probability
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.
Cite
@article{arxiv.math/0210090,
title = {Random complex zeroes, I. Asymptotic normality},
author = {Mikhail Sodin and Boris Tsirelson},
journal= {arXiv preprint arXiv:math/0210090},
year = {2007}
}
Comments
26 pages. Version 2 (final): the end of the proof corrected (sections 3.2, 3.3); small insertions to Introduction and References