Random comples zeroes, II. Perturbed lattice
Mikhail Sodin, Boris Tsirelson,
"Random comples zeroes, II. Perturbed lattice."
Israel Journal of Mathematics 152, 105-124 (2006).
Available online (free of charge) from e-print archive (USA):
or its Israeli mirror:
A research paper, 20 pages, bibl. 14 refs.
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 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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