Levy's phenomenon for analytic functions in the polydisc
  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. 
A. O. Kuryliak, O. B. Skaskiv, S. R. Skaskiv
math.CV