Lyapunov exponents for products of truncated orthogonal matrices

2025/05/08 by Dong Qichao, Qichao, Dong
Computer Science · Mathematics · #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2505.04928

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Non-asymptotic Results for Singular Values of Gaussian Matrix Products
• Fluctuations of β-Jacobi Product Processes
• Lyapunov exponent, universality and phase transition for products of random matrices

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• Easy estimates of Lyapunov exponents for random products of matrices
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• Non-asymptotic Results for Singular Values of Gaussian Matrix Products
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