Berry-Esseen type bounds for the matrix coefficients and the spectral radius of the left random walk on GLd(R)

TL;DR

This paper establishes convergence rates in the Central Limit Theorem for matrix coefficients and spectral radius of left random walks on GLd(R), under certain moment conditions, advancing understanding of their probabilistic behavior.

Contribution

It provides new Berry-Esseen type bounds for the spectral radius and matrix coefficients in the context of random walks on GLd(R), under exponential or polynomial moment assumptions.

Findings

Derived explicit convergence rates in CLT for spectral radius

Established bounds for matrix coefficients in random walks

Extended CLT results to broader moment conditions

Abstract

We give rates of convergence in the Central Limit Theorem for the coefficients and the spectral radius of the left random walk on GLd(R), assuming the existence of an exponential or polynomial moment.