Abstract
Simple exact expressions are derived for all the Lyapunov exponents of certainN-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 asN→∞. In the case of the time-ordered product integral of exp[N −1/2 dW], where the entries of theN×N matrixW(t) are independent standard Wiener processes, the exponents are equally spaced for fixedN and thus have a uniform distribution as N→∞.
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Communicated by O. E. Lanford
John S. Guggenheim Memorial Fellow. Research supported in part by NSF Grant MCS 80-19384
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Newman, C.M. The distribution of Lyapunov exponents: Exact results for random matrices. Commun.Math. Phys. 103, 121–126 (1986). https://doi.org/10.1007/BF01464284
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DOI: https://doi.org/10.1007/BF01464284