Infinite Products of Random Isotropically Distributed Matrices
A.S. Il'yn, V.A. Sirota, K.P. Zybin
TL;DR
This paper develops a formalism to analyze the statistical properties, including Lyapunov exponents, of infinite products of random isotropically distributed matrices, relevant to physics and chaos theory.
Contribution
It introduces a new formalism for calculating Lyapunov spectra of infinite matrix products with isotropic distributions, applicable to continuous and discrete cases.
Findings
Formalism for Lyapunov spectrum calculation
Applicable to continuous processes with finite correlation time
Useful for turbulent transport and chaos analysis
Abstract
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
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