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Random complex zeroes, II. Perturbed lattice

Mikhail Sodin·Boris Tsirelson
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Abstract

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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Mikhail Sodin, Boris Tsirelson. 2005-10-14. Random complex zeroes, II. Perturbed lattice. https://arxiv.org/abs/math/0309449

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