Random matrices and Lyapunov coefficients regularity

2013/11/20 by Giovanni Gallavotti, Gallavotti, Giovanni
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1311.5129

openalex publication_date 2013/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Analyticity and other properties of the largest or smallest Lyapunov exponent of a product of real matrices with a "cone property" are studied as functions of the matrices entries, as long as they vary without destroying the cone property. The result is applied to stability directions, Lyapunov coefficients and Lyapunov exponents of a class of products of random matrices and of dynamical systems. The method is based on the classical theory of the Mayer series in Statistical Mechanics of rarefied gases.

Citations

• Products of Random Matrices

Related

• Analyticity of the Lyapunov exponents of random products of matrices
• Upper bound on the regularity of the Lyapunov exponent for random products of matrices
• Easy estimates of Lyapunov exponents for random products of matrices
• Equality of Lyapunov and stability exponents for products of isotropic random matrices
• Continuity of the Lyapunov exponents of random matrix products