Levy's phenomenon for analytic functions in the polydisc

TL;DR

This paper establishes a sharp analogue of Wiman's inequality for random analytic functions in the polydisc, extending classical results to a multivariable setting.

Contribution

It introduces a new sharp inequality for random analytic functions in the polydisc, generalizing Wiman's inequality to multiple complex variables.

Findings

Proves a sharp analogue of Wiman's inequality in the polydisc.

Extends classical inequalities to multivariable analytic functions.

Provides bounds for the growth of random analytic functions in several complex variables.

Abstract

In this paper we prove some analogue of Wiman's type inequality for random analytic functions in the polydisc $\mathbb{D}^p=\{z\in\mathbb{C}^p\colon |z_j|<1, j\in\{1,\ldots,p\}\},\ p\in\mathbb{Z}_+$. The obtained inequality is sharp.