Random complex zeroes, II. Perturbed lattice

Mikhail Sodin*, Boris Tsirelson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function ψ(z) = ∑k=0ηk z k/√k! where η0, η1, ... 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.

Original languageEnglish
Pages (from-to)105-124
Number of pages20
JournalIsrael Journal of Mathematics
Volume152
DOIs
StatePublished - 2006

Funding

FundersFunder number
Israel Science Foundation of the Israel Academy of Sciences and Humanities

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