Abstract
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.
Original language | English |
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Pages (from-to) | 466-472 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 396 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2012 |
Subject classification (UKÄ)
- Mathematics
Free keywords
- Gaussian analytic functions
- Paley-Wiener
- Gap probabilities