Abstract
We prove strong clustering of k-point correlation functions of of Gaussian Entire Functions. In the course of the proof, we also obtain universal local bounds for k-point functions of of arbitrary nondegenerate Gaussian analytic functions. In the second part of the paper, we show that strong clustering yields the asymptotic normality of fluctuations of some linear statistics of of Gaussian Entire Functions, in particular, of the number of in measurable domains of large area. This complements our recent results from the paper Fluctuations in random complex zeroes (arXiv:1003.4251v1).
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