Invariant functions for the Lyapunov exponents of random matricesстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация: A new approach to the study of Lyapunov exponents of random
matrices is presented. We prove that any family of nonnegative (d×d)-
matrices has a continuous concave invariant functional on R^d_+. Under some
standard assumptions on the matrices, this functional is strictly positive,
and the coefficient corresponding to it is equal to the largest Lyapunov
exponent. As a corollary we obtain asymptotics for the expected value
of the logarithm of norms of matrix products and of their spectral radii.
Another corollary gives new upper and lower bounds for the Lyapunov
exponent, and an algorithm for computing it for families of nonnegative
matrices. We consider possible extensions of our results to general nonnegative
matrix families and present several applications and examples.