随机复零点的关联函数：强聚类和局部普适性
Correlation functions for random complex zeroes: strong clustering and local universality
摘要：
证明了高斯整函数零点的k点关联函数的强聚类性。在证明过程中，我们还得到了任意非退化高斯解析函数零点的k点函数的泛局部界。在本文的第二部分中，我们证明了强聚类产生的高斯整函数的零点的一些线性统计量的波动的渐近正态性，特别是，在可测量的大区域的零点的数量。这补充了我们最近在论文“Fluctuations in random complex zeroes”（arXiv：1003.4251v1）中的结果。
英文摘要：
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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