Local limit theorem for the operator norm of products of random matrices

Abstract

We prove a local limit theorem for the quantity $\Vert g_n\cdots g_1\Vert$, where $g_1,g_2,\dots$ is a sequence of independent and identically distributed random invertible square matrices. The norm $\Vert \cdot \Vert$ is arbitrary and we make no proximality assumption.

63 pages, 1 figure, a few misprints corrected