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The distribution of Lyapunov exponents: Exact results for random matrices. (English) Zbl 0593.58051
Author’s summary: ”Simple exact expressions are derived for all the Lyapunov exponents of certain N-dimensional stochastic linear dynamical systems. In the case of the product of independent random matrices, each of which has independent Gaussian entries with mean zero and variance 1/N, the exponents have an exponential distribution as \(N\to \infty\). In the case of the time-ordered product integral of \(\exp [N^{-1/2}dW]\), where the entries of the \(N\times N\) matrix W(t) are independent standard Wiener processes, the exponents are equally spaced for fixed N and thus have a uniform distribution as \(N\to \infty.''\)
Reviewer: G.Warnecke

MSC:
58J70 Invariance and symmetry properties for PDEs on manifolds
60G07 General theory of stochastic processes
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