Generalized Lyapunov exponents for products of correlated random matrices

We give the exact expressions for the generalized Lyapunov exponents of products of random matrices extracted with a Markovian rule. In analogy to the uncorrelated case, these expressions are obtained via a replica trick method, and exponents are given by the largest eigenvalue in modulus of appropriate matrices. As an application we study the distribution of the electronic de conductance in the random dimer model, which is of interest because it possesses an extended state. We find that in the vicinity of this state the distribution is lognormal and characterized by one single parameter, which is the localization length.