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Random complex zeroes, I. Asymptotic normality

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Abstract

We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of zeroes.

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Authors and Affiliations

  1. School of Mathematics, Tel Aviv University, Ramal Aviv, 69978, Tel Aviv, Israel

    Mikhail Sodin & Boris Tsirelson

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  1. Mikhail Sodin
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  2. Boris Tsirelson
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Correspondence to Mikhail Sodin.

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Supported by the Israel Science Foundation of the Israel Academy of Sciences and Humanities.

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Sodin, M., Tsirelson, B. Random complex zeroes, I. Asymptotic normality. Israel J. Math. 144, 125–149 (2004). https://doi.org/10.1007/BF02984409

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  • DOI: https://doi.org/10.1007/BF02984409

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