Abstract
Upper bounds for the maximal Lyapunov exponent,E, of a sequence of matrix-valued random variables are easy to come by asE is the infimum of a real-valued sequence. We shall show that under irreducibility conditions similar to those needed to prove the Perron-Frobenius theorem, one can find sequences which increase toE. As a byproduct of the proof we shall see that we may replace the matrix norm with the spectral radius when computingE in such cases. Finally, a sufficient condition for transience of random walk in a random environment is given.
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Key, E.S. Lower bounds for the maximal Lyapunov exponent. J Theor Probab 3, 477–488 (1990). https://doi.org/10.1007/BF01061263
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DOI: https://doi.org/10.1007/BF01061263