The Lyapunov Spectrum of a Continuous Product of Random Matrices

Abstract

We expose a functional integration method for the averaging of continuous products ${\hat{P}}_t$ of $N\times N$ random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum of ${\hat{P}}_t$. This problem is relevant to the study of the statistical properties of various disordered physical systems, and specifically to the computation of the multipoint correlators of a passive scalar advected by a random velocity field. Apart from these applications, our method provides a general setting for computing statistical properties of linear evolutionary systems subjected to a white noise force field.

Latex, 9 pages

References in corpus (4)

• Statistics of a Passive Scalar Advected by a Large-Scale 2D Velocity Field: Analytic Solution
• On the distribution of transmission eigenvalues in disordered wires
• Passive scalar convection in 2D long-range delta-correlated velocity field: Exact results
• Statistics of the One-Electron Current in a One-Dimensional Mesoscopic Ring at Arbitrary Magnetic Fields

Cited by in corpus (10)

• Particles and fields in fluid turbulence
• Slow modes in passive advection
• Turbulent Decay of a Passive Scalar in Batchelor Limit: Exact Results from a Quantum-Mechanical Approach
• Statistical Properties of the T-exponential of Isotropically Distributed Random Matrices
• Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis
• Dissipation statistics of a passive scalar in a multidimensional smooth flow
• Passive advection in nonlinear medium
• Infinite Products of Random Isotropically Distributed Matrices
• Notes about Passive Scalar in Large-Scale Velocity Field
• Counting the exponents of single transfer matrices