Gap probabilities for the cardinal sine

Details Gap probabilities for the cardinal sine Gap probabilities for the cardinal sine

2011-08-15

arxiv.org/abs/1108.2983v1

Mathematics

Complex Variables

8 pages, 1 figure

Scientific paper

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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