Random complex zeroes, III. Decay of the hole probability

Mikhail Sodin*, Boris Tsirelson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The 'hole probability' that a random entire function ψ(z) = Σk=0 ζk zk/ √k!, where ζ0, ζ1,... are Gaussian i.i.d. random variables, has no zeroes in the disc of radius r decays as exp(-cr 4) for large r.

Original languageEnglish
Pages (from-to)371-379
Number of pages9
JournalIsrael Journal of Mathematics
Volume147
DOIs
StatePublished - 2005

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