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Gap probabilities for the cardinal sine

Antezana, Jorge ; Buckley, Jeremiah ; Marzo, Jordi and Olsen, Jan-Fredrik LU (2012) In Journal of Mathematical Analysis and Applications 396(2). p.466-472
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.
Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Gaussian analytic functions, Paley-Wiener, Gap probabilities
in
Journal of Mathematical Analysis and Applications
volume
396
issue
2
pages
466 - 472
publisher
Elsevier
external identifiers
  • wos:000315246900006
  • scopus:84865564983
ISSN
0022-247X
DOI
10.1016/j.jmaa.2012.06.022
language
English
LU publication?
yes
id
cd58bf4e-c817-44d5-9560-0fb5971dbb8b (old id 3567993)
date added to LUP
2016-04-01 15:02:03
date last changed
2022-01-28 03:43:12
@article{cd58bf4e-c817-44d5-9560-0fb5971dbb8b,
  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.}},
  author       = {{Antezana, Jorge and Buckley, Jeremiah and Marzo, Jordi and Olsen, Jan-Fredrik}},
  issn         = {{0022-247X}},
  keywords     = {{Gaussian analytic functions; Paley-Wiener; Gap probabilities}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{466--472}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Mathematical Analysis and Applications}},
  title        = {{Gap probabilities for the cardinal sine}},
  url          = {{http://dx.doi.org/10.1016/j.jmaa.2012.06.022}},
  doi          = {{10.1016/j.jmaa.2012.06.022}},
  volume       = {{396}},
  year         = {{2012}},
}