Analytic Dependence of the Lyapunov Moment Function and the Projective Stationary Measure for Random Matrix Products

2025/12/04 by Christopher Chalhoub, Chalhoub, Christopher, Vincent P. H. Goverse +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2512.05034

openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28

Abstract

We consider the product of i.i.d. random matrices sampled according to a probability measure μ supported on a strongly irreducible and proximal subset of a compact set S⊂ GL(d,ℝ). We establish the local analyticity of the Lyapunov moment function and the unique stationary measure on the projective space with respect to μ in the total variation topology. As a consequence, we obtain the analyticity of the asymptotic variance and all higher-order Lyapunov moments.

Citations

• Analyticity of the Lyapunov exponents of random products of matrices
• Continuity of the Lyapunov exponents of random matrix products
• Stationary probability measures on projective spaces 2: the critical case
• Stationary probability measures on projective spaces for block-Lyapunov dominated systems
• Precise large deviation asymptotics for products of random matrices
• Large deviation principle for random matrix products
• Random matrix products and measures on projective spaces

Related

• Continuity of the Lyapunov exponents of random matrix products
• Analyticity of the Lyapunov exponents of random products of matrices
• Stationary probability measures on projective spaces 2: the critical case
• Random products of matrices: a dynamical point of view
• Random matrices and Lyapunov coefficients regularity