The Lyapunov Spectrum of a Continuous Product of Random Matrices

Details The Lyapunov Spectrum of a Continuous Product of Random Matrices The Lyapunov Spectrum of a Continuous Product of Random Matrices

1996-10-27

arxiv.org/abs/cond-mat/9610192v1

J. Stat. Phys. 85 (1996) 489-499

Physics

Condensed Matter

Disordered Systems and Neural Networks

Latex, 9 pages

Scientific paper

10.1007/BF02174216

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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