Continuity of the Lyapunov exponents of random matrix products

2023/05/10 by Artur Avila, Avila, Artur, Alex Eskin +3 · 3 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #advanced mathematical theories #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2305.06009

Abstract

We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally, the Lyapunov exponents of the random product defined by any compactly supported probability distribution on GL(d) vary continuously with the distribution, in a natural topology corresponding to weak^*-closeness of the distributions and Hausdorff-closeness of their supports.

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• Analytic Dependence of the Lyapunov Moment Function and the Projective Stationary Measure for Random Matrix Products
• Obstructions to the regularity of the Lyapunov exponents for non-compact random Schrödinger cocycles
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