Bounds on Lyapunov exponents

05/08/2019

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by   David Sutter, et al.

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Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. Here we derive an analytical upper and lower bound for the maximal and minimal Lyapunov exponent, respectively. The bounds are tight in the commutative case and other scenarios. They can be expressed in terms of an optimization problem that only involves single matrices rather than large products. The upper bound for the maximal Lyapunov exponent can be evaluated efficiently via the theory of convex optimization.