Gap probabilities for the cardinal sine

[摘要] We study the zero sets of random analytic functions generated by a sum of the cardinal sine functions which form an orthonormal 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. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Gaussian analytic functions;Paley-Wiener;Gap probabilities