Spectral representation of correlation functions for zeros of Gaussian power series with stationary coefficients

2025/01/07 by Tomoyuki Shirai, Shirai, Tomoyuki
Environmental Science · Mathematics · #30B20 #30C15 #60G15 #60G55 #Analysis of environmental and stochastic processes #Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2501.03704

openalex publication_date 2025/01/07 · openalex created_date 2025/01/09 · openalex updated_date 2026/07/28

Abstract

We analyze Gaussian analytic functions (GAFs) defined as power series with coefficients modeled by discrete stationary Gaussian processes, utilizing their spectral measures. We revisit some limit theorems for random analytic functions and examine some examples of GAFs through numerical computations. Furthermore, we provide an integral representation of the n-point correlation functions of the zero sets of GAFs in terms of the spectral measures of the underlying coefficient Gaussian processes.

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