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

2009/12/11 by Péter Major, Peter Major, Major, Peter
Mathematics · #60E15 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60E15

paper · pdf · doi:10.48550/arxiv.0912.2279

arxiv created 2009/12/11 · openalex publication_date 2009/12/11 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. \

Citations

• An estimate on the maximum of a nice class of stochastic integrals

Related

• A tail estimate for empirical processes of multivariate Gaussian under general dependence
• General upper and lower tail estimates using Malliavin calculus and Stein's equations
• An elementary proof of anti-concentration for degree two non-negative Gaussian polynomials
• Large deviations for the empirical measure of random polynomials: revisit of the Zeitouni-Zelditch theorem
• A counterexample for equivalence result between tails behavior and Grand Lebesgue Spaces norms