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.
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