GENERALIZED LYAPUNOV EXPONENTS FOR PRODUCTS OF CORRELATED RANDOM MATRICES

We give the exact expressions for the generalized Lyapunov exponents o f products of random matrices extracted with a Markovian rule. In anal ogy to the uncorrelated case, these expressions are obtained via a rep lica trick method, and exponents are given by the largest eigenvalue i n modulus of appropriate matrices. As an application we study the dist ribution of the electronic de conductance in the random dimer model, w hich is of interest because it possesses an extended state. We find th at in the vicinity of this state the distribution is lognormal and cha racterized by one single parameter, which is the localization length.