Statistical Properties of the T-exponential of Isotropically Distributed Random Matrices

TL;DR

This paper introduces a functional method to compute averages of the time-ordered exponential of isotropic random matrices, applicable to non-Gaussian processes, with implications for turbulence and energy flow analysis.

Contribution

It develops a novel approach for calculating statistical properties of the T-exponential for non-Gaussian isotropic matrix processes.

Findings

Derived Lyapunov exponents for the process

Calculated higher correlation functions

Applicable to non-Gaussian statistical analysis

Abstract

A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random $N\times N$ matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and higher correlation functions of the T-exponent are derived from the statistical properties of the process. The approach may be of use in a wide range of physical problems. For example, in theory of turbulence the account of non-gaussian statistics is very important since the non-Gaussian behavior is responsible for the time asymmetry of the energy flow.