Random complex zeroes, II. Perturbed lattice
Complex Variables
2007-05-23 v2 Mathematical Physics
math.MP
Probability
Abstract
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 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.
Cite
@article{arxiv.math/0309449,
title = {Random complex zeroes, II. Perturbed lattice},
author = {Mikhail Sodin and Boris Tsirelson},
journal= {arXiv preprint arXiv:math/0309449},
year = {2007}
}
Comments
21 pages. Version 2 (final): the introduction is re-designed, the bibliography is updated; tiny changes in other sections