We show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function psi(z) = Sigma(infinity)(k=0)zeta(k)z(k)/root k! where zeta 0, zeta 1,... are independent standard complex-valued Gaussian variables) can be regarded as a random perturbation of a lattice in the plane. The distribution of the distances between the zeroes and the corresponding lattice points is shift-invariant and has a Gaussian-type decay of the tails.
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