Bornes à la Berry-Esseen pour la distance du chi-deux dans le théorème central limite : une approche markovienne

Abstract

Comments welcome.\\New version: relevant reference added, introduction modified.This article presents a new proof of the rate of convergence to the normal distribution of sums of independent, identically distributed random variables in chi-square distance, which was also recently studied in \cite{BobkovRenyi}. Our method consists of taking advantage of the underlying time non-homogeneous Markovian structure and studying the spectral properties of the non-reversible transition operator, which allows to find the optimal rate in the convergence above under matching moments assumptions. Our main assumption is that the random variables involved in the sum are independent and have polynomial density; interestingly, our approach allows to relax the identical distribution hypothesis