Estimates on the tail behavior of Gaussian polynomials. The discussion of a result of Latala

Abstract

In this paper a result of Latala about the tail behavior of Gaussian polynomials will be discussed. Latala proved an interesting result about this problem in paper [2]. But his proof applied an incorrect statement at a crucial point. Hence the question may arise whether the main result of paper [2] is valid. The goal of this paper is to settle this problem by presenting such a proof where the application of the erroneous statement is avoided. I discuss the proofs in detail even at the price of a longer text and try to give such an explanation that reveals the ideas behind them better than the original paper. \