Gap probabilities for the cardinal sine

Summary, in English

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.

• Författare: Jorge Antezana; Jeremiah Buckley; Jordi Marzo; Jan-Fredrik Olsen
• Avdelning/ar: Matematik (naturvetenskapliga fakulteten)
• Publiceringsår: 2012
• Språk: Engelska
• Sidor: 466-472
• Publikation/Tidskrift/Serie: Journal of Mathematical Analysis and Applications
• Volym: 396
• Issue: 2
• Länkar: http://dx.doi.org/10.1016/j.jmaa.2012.06.022
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: Gaussian analytic functions; Paley-Wiener; Gap probabilities
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 0022-247X