Year: 2011
Type: preprint
Abstract: We review a result obtained with Andrew Ledoan and Marco Merkli. Consider a random analytic function $f(z) = \sum_{n=0}^{\infty} a_n X_n z^n$, where the $X_n$'s are i.i.d., complex valued random variables with mean zero and unit variance, and the coefficients $a_n$ are non-random and chosen so that the variance transforms covariantly under conformal transformations of the domain. If the $X_n$'s are Gaussian, this is called a Gaussian analytic function (GAF). We prove that, even if the coefficients are not Gaussian, the zero set converges in distribution to that of a GAF near the boundary of the domain.
Source: arXiv (Cornell University)
Author: Starr, Shannon
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4301518330