Correlation functions for random complex zeroes: strong clustering and local universality

Details Correlation functions for random complex zeroes: strong clustering and local universality Correlation functions for random complex zeroes: strong clustering and local universality

2010-05-22

arxiv.org/abs/1005.4113v1

Physics

Mathematical Physics

22 pages

Scientific paper

We prove strong clustering of k-point correlation functions of zeroes of Gaussian Entire Functions. In the course of the proof, we also obtain universal local bounds for k-point functions of zeroes 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 zeroes of Gaussian Entire Functions, in particular, of the number of zeroes 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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