English

Gap probabilities for the cardinal sine

Complex Variables 2011-08-16 v1 Probability

Abstract

We study the zero set of random analytic functions generated by a sum of the cardinal sine functions that form an orthogonal 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.

Keywords

Cite

@article{arxiv.1108.2983,
  title  = {Gap probabilities for the cardinal sine},
  author = {Jorge Antezana and Jeremiah Buckley and Jordi Marzo and Jan-Fredrik Olsen},
  journal= {arXiv preprint arXiv:1108.2983},
  year   = {2011}
}

Comments

8 pages, 1 figure

R2 v1 2026-06-21T18:50:33.218Z