2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99882We 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.21 pages. Version 2 (final): the introduction is re-designed, the bibliography is updated; tiny changes in other sectionsComplex VariablesMathematical PhysicsProbability30B20; 30C15, 60G60, 82B10text