Mikhail Sodin, Boris Tsirelson,
"Random comples zeroes, II. Perturbed lattice."
math.CV/0309449.
Israel Journal of Mathematics 152, 105-124 (2006).
Available online (free of charge) from e-print archive (USA):
arXiv.org/abs/math.CV/0309449/
or its Israeli mirror:
il.arXiv.org/abs/math.CV/0309449/

A research paper, 20 pages, bibl. 14 refs.

We show that the 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!) can be regarded as a random perturbation of a lattice in the plane. The distribution of the distances between the zeroes and the lattice points is shift-invariant and has a Gaussian-type decay of the tails.

1. Introduction.
1. A class of metrics in R^d.
2. Whitney-type partitions of unity.
3. The main lemma.
4. Tying zeroes of an entire function to the lattice points.
5. Probabilistic arguments.
6. Final technicalities.