Mikhail Sodin, Boris Tsirelson,
"Random comples zeroes, I. Asymptotic normality."
math.CV/0210090.
Israel Journal of Mathematics 144, 125-149 (2004).
Available online (free of charge) from e-print archive (USA):
arXiv.org/abs/math.CV/0210090/
or its Israeli mirror:
il.arXiv.org/abs/math.CV/0210090/

A research paper, 25 pages, bibl. 28 refs.

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.

1. Introduction and the main result.
1. Geometrical description of models.
2. Asymptotic normality for non-linear functionals of Gaussian processes.
3. Asymptotic normality for chaotic analytic zero points.