Asymptotic moment growth for products of correlated random matrices and applications to disordered conductors

The Lyapunov exponent of a product of random matrices displays finite-size fluctuations that can be characterized by the asymptotic growth rates of the product’s moments. Through a generalization of the replica method developed for products of uncorrelated random matrices we derive here expressions for computing the moments growth rate in the case of Markov correlated matrices. We use our results for investigating some statistical properties of the d.c. conductance in a model for conducting linear polymer, the random dimer model, finding that it displays universal fluctuations in the vicinity of the extended states.