TY - JOUR

T1 - Correlation Functions for Random Complex Zeroes

T2 - Strong Clustering and Local Universality

AU - Nazarov, F.

AU - Sodin, M.

N1 - Funding Information:
F.N. is partially supported by the National Science Foundation, DMS grant 0501067.
Funding Information:
M.S. is partially supported by the Israel Science Foundation of the Israel Academy of Sciences and Humanities, grant 171/07.

PY - 2012/2

Y1 - 2012/2

N2 - 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".

AB - 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".

UR - http://www.scopus.com/inward/record.url?scp=84856652018&partnerID=8YFLogxK

U2 - 10.1007/s00220-011-1397-4

DO - 10.1007/s00220-011-1397-4

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AN - SCOPUS:84856652018

SN - 0010-3616

VL - 310

SP - 75

EP - 98

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -