Gap probabilities for the cardinal sine
We study the zero set of random analytic functions generated by a sum of the cardinal sine functions which 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 bound...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:196685 |
| Acesso em linha: | https://ddd.uab.cat/record/196685 |
| Access Level: | acceso abierto |
| Palavra-chave: | Funcions analítiques Probabilitats 519.1 - Teoria general de l'anàlisi combinatòria. Teoria de grafs |
| Resumo: | We study the zero set of random analytic functions generated by a sum of the cardinal sine functions which 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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