The Study of Gaussian Analytic Functions and their Zeroes

我们对高斯解析函数（Gauss analytic functions，GAF）的研究很感兴趣。特别地，我们研究了它们的零点集的性质。我们定义一个随机变量是一个特定的GAF的半径为r的磁盘内的零的数量，并调查这个随机变量的性质，因为r趋于收敛的半径。然后，目标是找到方差的渐近表达式，并证明这个随机变量是否满足中心极限定理。

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.