## B. Tsirelson | ## Random comples zeroes, II. Perturbed lattice | ## Recent works |

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.

- Introduction.
- A class of metrics in
R
^{d}. - Whitney-type partitions of unity.
- The main lemma.
- Tying zeroes of an entire function to the lattice points.
- Probabilistic arguments.
- Final technicalities.

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