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Correlation functions for zeros of a Gaussian power series and Pfaffians. (English) Zbl 1291.60102
Summary: We show that the zeros of the random power series with i.i.d. real Gaussian coefficients form a Pfaffian point process. We also show that the product moments for absolute values and signatures of the power series can also be expressed by Pfaffians.

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
30B20 Random power series in one complex variable
60G15 Gaussian processes
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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