Berry-Esseen bounds with targets and Local Limit Theorems for products of random matrices

Tien-Cuong Dinh, Lucas Kaufmann, Hao Wu

Let $\mu$ be a probability measure on ${\text{GL}}_d(\mathbb{R})$ and denote by $S_n:=g_n\cdots g_1$ the associated random matrix product, where $g_j$'s are i.i.d.'s with law $\mu$. We…