Gaussian and non-Gaussian distributed random analytical and entire functions

TL;DR

This paper studies the properties of complex Gaussian and non-Gaussian random entire functions, determining their convergence domains and characteristics, and proving these are almost surely deterministic.

Contribution

It provides a comprehensive analysis of the domain of convergence and order/type of both Gaussian and non-Gaussian random entire functions, establishing their deterministic nature.

Findings

Characteristics are deterministic with probability one.

Explicit calculations of radius of convergence, order, and type.

Examples confirming the sharpness of results.

Abstract

We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important characteristics: order and type. As a consequence we deduce that all the mentioned characteristics, under very natural conditions, are deterministic (non-random) with probability one and we calculate them. Moreover we exhibit some examples to show the exactness of the obtained results.