Lyapunov exponents for products of truncated orthogonal matrices

Abstract

This article gives a non-asymptotic analysis of the largest Lyapunov exponent of truncated orthogonal matrix products. We prove that as long as N, the number of terms in product, is sufficiently large, the largest Lyapunov exponent is asymptotically Gaussian. Furthermore, the sum of finite Lyapunov exponent is asymptotically Gaussian, where we use Weingarten Calculus.