Distribution of Normalized Zero-Sets of Random Entire Functions with Small Random Perturbation

TL;DR

This paper investigates how small random perturbations affect the distribution of zeros in random entire functions, extending previous results to include these perturbations.

Contribution

It introduces an extension of earlier work to analyze the zero-set distribution under small random perturbations in entire functions.

Findings

Distribution of zeros is stable under small perturbations.

Extended the theoretical framework to include perturbations.

Results confirm robustness of zero distribution patterns.

Abstract

In this paper, we extend our earlier result (see [Y-2008]) on the distribution of normalized zero-sets of random entire functions to random entire functions with small random perturbation.