A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory

We use ergodic theory to prove a quantitative version of a theorem of M.A. Berger and Y. Wang, which relates the joint spectral radius of a set of matrices to the spectral radii of finite products of those matrices. The proof rests on a structure theorem for continuous matrix cocycles over minimal homeomorphisms having the property that all forward products are uniformly bounded.