B. Tsirelson

Random comples zeroes, II. Perturbed lattice

Recent works

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.

  1. Introduction.
  2. A class of metrics in Rd.
  3. Whitney-type partitions of unity.
  4. The main lemma.
  5. Tying zeroes of an entire function to the lattice points.
  6. Probabilistic arguments.
  7. Final technicalities.
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