Levy's phenomenon for analytic functions in the polydisc

Abstract

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