Random zeros entire functions

TL;DR

This paper introduces methods to construct entire functions with randomly distributed zeros, including cases with simple zeros and zeros with random multiplicities, expanding understanding of random zero configurations.

Contribution

It presents novel constructions for entire functions with prescribed random zero sets, covering both simple and multiple zeros scenarios.

Findings

Constructed entire functions with random zeros

Analyzed cases with simple zeros and multiple zeros

Provided frameworks for random zero configurations

Abstract

We propose the construction of entire functions with a given random collection of zeros. There are considered two particular cases. In the first one we are dealing with simple zeros. And the second corresponds to random zeros with random multiplicity.