Work

Hole phenomenon of Gaussian analytic functions with power-exponential weights

Year: 2026

Type: article

Abstract: We establish the hole phenomenon for the Gaussian analytic function [Formula: see text] associated with the power-exponential weight [Formula: see text] on [Formula: see text], where [Formula: see text]. Under the condition that [Formula: see text] has no zeros in [Formula: see text], the scaled zero counting measure converges to a limiting measure [Formula: see text] vaguely in distribution. This limit exhibits a forbidden [Formula: see text] which zeros asymptotically avoid. This generalizes the remarkable discovery of Ghosh and Nishry for the Gaussian entire function (the case [Formula: see text]), who first revealed this striking conditional convergence and the emergence of a hole. Our analysis extends their phenomenon to the entire family of power-exponential weights.

Source: International Journal of Mathematics

DOI: 10.1142/s0129167x26500588

Author: Yun-Heng Du

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G7519385794