Abstract
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→∞. In the case of the time-ordered product integral of exp[N-1/2dW], where the entries of the N×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→∞.
Original language | English (US) |
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Pages (from-to) | 121-126 |
Number of pages | 6 |
Journal | Communications In Mathematical Physics |
Volume | 103 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1986 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics