Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

Abstract

Let $(g_n{)}_{n\ge 1}$ be a sequence of independent and identically distributed positive random $d\times d$ matrices and consider the matrix product $G_n:=g_n\dots g_1$. Under suitable conditions, we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and moderate deviation expansions of Cramér type, for the matrix norm $\Vert G_n\Vert$ of $G_n$, for its $(i,j)$-th entry $G_n^{i,j}$, and the and for its spectral radius $\rho (G_n)$.

Cited by in corpus (2)

• Limit theorems for the coefficients of random walks on the general linear group
• Berry-Esseen bound and Local Limit Theorem for the coefficients of products of random matrices