Gap probabilities for the cardinal sine

Jorge Antezana, Jeremiah Buckley, Jordi Marzo, Jan-Fredrik Olsen

Research output: Contribution to journalArticlepeer-review

7 Citations (SciVal)

Abstract

We study the zero sets of random analytic functions generated by a sum of the cardinal sine functions which form an orthonormal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero in a bounded interval decays exponentially as a function of the length. (C) 2012 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)466-472
JournalJournal of Mathematical Analysis and Applications
Volume396
Issue number2
DOIs
Publication statusPublished - 2012

Subject classification (UKÄ)

  • Mathematics

Keywords

  • Gaussian analytic functions
  • Paley-Wiener
  • Gap probabilities

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