Gap probabilities for the cardinal sine
classification
🧮 math.CV
math.PR
keywords
cardinalfunctionssinezeroanalyticasymptoticbasisbounded
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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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