Mikhail Sodin, Boris Tsirelson,
"Random comples zeroes, III. Decay of the hole probability."
math.CV/0312258.
Israel Journal of Mathematics 147, 371-379 (2005).
Available online (free of charge) from e-print archive (USA):
arXiv.org/abs/math.CV/0312258/
or its Israeli mirror:
il.arXiv.org/abs/math.CV/0312258/

A research paper, 9 pages, bibl. 6 refs.

By a hole we mean a disc that contains no flat chaotic analytic zero points (i.e. zeroes of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!). A given disc of radius r has a probability of being a hole, - the hole probability. We show that for large r the hole probability decays as exp(-cr⁴).

1. Introduction.
1. Proof of the lower bound in Theorem 1.
2. Large deviations.
3. Mean lower bound.
4. Proof of Theorem 2.