The hole probability for Gaussian entire functions

Alon Nishry*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Consider the random entire function, where the øn are independent standard complex Gaussian coefficients, and the an are positive constants, which satisfy. We study the probability PH(r) that f has no zeroes in the disk { {pipe}z{pipe} < r} (hole probability). Assuming that the sequence an is logarithmically concave, we prove that log PH(r) = -S(r)+o(S(r)), where, and r tends to ∞ outside a (deterministic) exceptional set of finite logarithmic measure.

Original languageEnglish
Pages (from-to)197-220
Number of pages24
JournalIsrael Journal of Mathematics
Volume186
Issue number1
DOIs
StatePublished - Nov 2011

Funding

FundersFunder number
Israel Science Foundation of the Israel Academy of Sciences and Humanities171/07

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