Random complex zeroes, II. Perturbed lattice

Details Random complex zeroes, II. Perturbed lattice Random complex zeroes, II. Perturbed lattice

2003-09-27

arxiv.org/abs/math/0309449v2

Israel Journal of Mathematics 152 (2006), 105-124.

Mathematics

Complex Variables

21 pages. Version 2 (final): the introduction is re-designed, the bibliography is updated; tiny changes in other sections

Scientific paper

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 random 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.

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