On Transfer Operators for Markovian Products of Invertible Random Matrices

Abstract

In this article we consider the Markovian products of invertible (not necessarily positive) matrices chosen from a strongly irreducible, contracting, finite set of matrices. We construct Markovian transfer operators and prove the spectral property which draws a connection between the top Lyapunov exponent associated to the random matrix product problem and the spectrum of the corresponding Markovian transfer operator.