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Random complex zeroes, II. Perturbed lattice

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Abstract

We show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function\(\psi (z) = \sum {_{k = 0}^\infty \zeta } k\frac{{z^k }}{{\sqrt {k!} }}\) where ζ0, ζ1, … 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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Authors and Affiliations

  1. School of Mathematics, Tel Aviv University, 69978, Tel Aviv, Israel

    Mikhail Sodin & Boris Tsirelson

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  1. Mikhail Sodin
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  2. Boris Tsirelson
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Correspondence to Mikhail Sodin.

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Supported by the Israel Science Foundation of the Israel Academy of Sciences and Humanities.

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Sodin, M., Tsirelson, B. Random complex zeroes, II. Perturbed lattice. Isr. J. Math. 152, 105–124 (2006). https://doi.org/10.1007/BF02771978

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  • DOI: https://doi.org/10.1007/BF02771978

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