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The Lyapunov Spectrum of a Continuous Product of Random Matrices

A. Gamba·I. V. Kolokolov
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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.

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A. Gamba, I. V. Kolokolov. 1996-10-27. The Lyapunov Spectrum of a Continuous Product of Random Matrices. https://doi.org/10.1007/bf02174216

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