We show that the flat chaotic analytic zero points (i.e. zeroes of a randomentire function whose Taylor coefficients are independent complex-valuedGaussian 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. Thedistribution of the distances between the zeroes and the lattice points isshift-invariant and has a Gaussian-type decay of the tails.
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