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...

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Detalles Bibliográficos
Autores: Antezana, Jorge, Buckley, Jeremiah, Marzo Sánchez, Jordi, Olsen, Jan-Fredrik
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:196685
Acceso en línea:https://ddd.uab.cat/record/196685
Access Level:acceso abierto
Palabra clave:Funcions analítiques
Probabilitats
519.1 - Teoria general de l'anàlisi combinatòria. Teoria de grafs
Descripción
Sumario: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.