Universality of correlations for random analytic functions (Q2895559)
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scientific article; zbMATH DE number 6052341
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Universality of correlations for random analytic functions |
scientific article; zbMATH DE number 6052341 |
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3 July 2012
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random analytic functions
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Gaussian analytic functions
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convergence in distribution
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zero sets
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math.PR
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Universality of correlations for random analytic functions (English)
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The author considers random analytic functions defined by choosing a coefficient sequence to be complex valued random variables with mean zero and unit variance. If the coefficient sequence is Gaussian then it is called a Gaussian analytic function. The main result proves convergence in distribution of the zero set of the random analytic functions for a sequence of neighborhoods converging to the boundary. For the proof he uses tools from probability theory and comlpex analysis such as the Lindeberg-Feller condition and Hurwitz's theorem.NEWLINENEWLINEFor the entire collection see [Zbl 1223.82001].
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