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arXiv · 1108.2983

Gap probabilities for the cardinal sine

Jorge Antezana·Jeremiah Buckley·Jordi Marzo·Jan-Fredrik Olsen
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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.

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Jorge Antezana, Jeremiah Buckley, Jordi Marzo, Jan-Fredrik Olsen. 2011-08-15. Gap probabilities for the cardinal sine. https://arxiv.org/abs/1108.2983

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