2012
DOI: 10.1016/j.jmaa.2012.06.022
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Gap probabilities for the cardinal sine

Abstract: a b s t r a c tWe 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.

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Cited by 12 publications
(21 citation statements)
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“…The first result we know of this kind is due to Antezana, Buckley, Marzo and Olsen [2] who showed that for the Gaussian process (X t ) t∈R with Cov(X t , X s ) =…”
Section: Brief Review Of Past Resultsmentioning
confidence: 99%
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“…The first result we know of this kind is due to Antezana, Buckley, Marzo and Olsen [2] who showed that for the Gaussian process (X t ) t∈R with Cov(X t , X s ) =…”
Section: Brief Review Of Past Resultsmentioning
confidence: 99%
“…Their proof of lower bound uses the result of [2] for the Paley-Wiener process. But we give a full proof of Theorem 1 as it is different and self-contained.…”
Section: Brief Review Of Past Resultsmentioning
confidence: 99%
“…A simple and interesting example is the cardinal sine covariance r(t) = sin(πt) t , which corresponds to indicator spectral density 1I [−π,π] . In an elegant recent work, Antezana, Buckley, Marzo and Olsen [2] give exponential upper and lower bounds for H f (N ) (see Theorem 3 below). Our research may be viewed as a an extension of their result to other stationary Gaussian processes.…”
Section: 1mentioning
confidence: 99%
“…where µ ∈ M + (T * ) is non-negative and there exists M ′ > 0 such that (2) for any interval I ⊂ (−a, a) : µ(I) ≤ M ′ |I|.…”
Section: Upper Bound: Proof Of Theoremmentioning
confidence: 99%
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