Convexity of the Lyapunov exponent Original Research Article

Let γ(p) be the maximal Lyapunov exponent for an independently and identically distributed (i.i.d). random product of matrices where each factor equals A with probability p and B with probability 1−p. Counterexamples show that the two conjectures of E. Key on the convexity and concavity of the function γ in the interval (0,1) are too general. Under suitable assumptions on A,B convexity and concavity of γ are proved.