"Computing the Lyapunov exponent for Random Matrix Products"

Abstract: Given two matrices A(1) and A(2), we can consider the random products A(i_1) A(i_2) ... A(i_n), for i_1, i_2, ... in {1,2}. The Lyapunov exponent L is the rate of growth of the norm of a typical such product, as n tends to infinity. In the case of positive matrices we propose a way to efficiently estimate L. For example, with the matrices A(1) = ( 2 1 //1 1) and A(2) = (3 1 // 2 1) we estimate that L = 1.1433110351029492458432518536555882994025 ...

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