The Study of Gaussian Analytic Functions and their Zeroes

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We are interested in the study of Gaussian analytic functions (GAFs). In particular, we study the properties of their zero sets. We define a random variable to be the number of zeroes inside a disk of radius r of a particular GAF and investigate the properties of this random variable as r tends to the radius of convergence. Then the goal is to find an asymptotic expression for the variance as well as proving whether or not this random variable satisfies a central limit theorem.