A universality property of Gaussian analytic functions
type: Item
instance of: scholarly article
title: A universality property of Gaussian analytic functions
zbMATH Open document ID: 1259.30002
author: M. Merkli
author: Shannon Starr
author: Andrew Ledoan
published in: Journal of Theoretical Probability
publication date: 2012-06-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1003.1951
review text: This paper deals with random analytic functions (RAF), a class of functions which contains also the well-studied Gaussian analytic functions (GAF) (see, e.g., [\textit{J. B. Hough} et al., Zeros of Gaussian analytic functions and determinantal point processes. Providence, RI: American Mathematical Society (AMS) (2008; Zbl 1190.60038)]). In the first section, the authors introduce their framework, they discuss some known results about these two families of functions and they state a theorem for the zero set of GAF due to \textit{Y. Peres} and \textit{B. Virág} [Acta Math. 194, No. 1, 1--35 (2005; Zbl 1099.60037)]. They also announce their main result concerning convergence in distribution of the zero set of non-Gaussian RAF to that of GAF when we move isometrically to the boundary of the domain. Section 2 is devoted to the proof of the main theorem by using the CLT and classical results in complex analysis. Finally, a simple application for a discrete family of RAF is provided in Section 3, including also the plots of two particular examples.
reviewed by: Stavros Vakeroudis
Mathematics Subject Classification ID: 30B20
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 6050429
zbMATH Keywords: random analytic functions
zbMATH Keywords: Gaussian analytic functions
zbMATH Keywords: zero set
MaRDI profile type: Publication
OpenAlex ID: W1974235832
arXiv ID: 1003.1951
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DOI: 10.1007/S10959-011-0356-5
description: scientific article; zbMATH DE number 6050429