Edgeworth Expansion and Large Deviations for the Coefficients of Products of Positive Random Matrices

Consider the matrix products $G_n := g_n \cdots g_1$, where $(g_n)_{n \geq 1}$ is a sequence of independent and identically distributed positive random $d \times d$ matrices. Under the optimal third moment condition, we first establish a Berry--Esseen theorem and an Edgeworth expansion for the $(i,j