Products of Random Matrices

Abstract

Part of the one dimensional or quasi-one dimensional theory of localization can be reduced to the study of products of random matrices. One of the most important result in this direction is the extension to matrix valued random variables of the strong law of large numbers. Unfortunately the identification of the limit (called the Lyapunov exponent) is more complicated than in the classical case of real valued random variables. In particular this limit can no longer be written as a single expectation. Moreover its determination involves the computation of some invariant measure on the projective space. We only assume that the reader has a minimal background in classical probability theory. Most of the material presented in this chapter is self contained.