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

TL;DR

This paper revisits Latala's result on the tail behavior of Gaussian polynomials, providing a corrected proof that avoids previous errors and clarifies the underlying ideas.

Contribution

It offers a rigorous, error-free proof of Latala's main result on Gaussian polynomial tail estimates, enhancing understanding of the proof techniques.

Findings

Confirmed the validity of Latala's tail behavior result

Provided a detailed, corrected proof avoiding previous errors

Enhanced clarity of the proof ideas and methodology

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. \