Lyapunov exponents for products of truncated orthogonal matrices

TL;DR

This paper analyzes the largest Lyapunov exponent of products of truncated orthogonal matrices, showing it is asymptotically Gaussian for large N using non-asymptotic methods and Weingarten Calculus.

Contribution

It provides a non-asymptotic analysis and proves the asymptotic Gaussianity of the largest Lyapunov exponent for truncated orthogonal matrix products.

Findings

Largest Lyapunov exponent is asymptotically Gaussian for large N

Sum of finite Lyapunov exponents is asymptotically Gaussian

Uses Weingarten Calculus for analysis

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.