The weak Bernoulli property for matrix Gibbs states

We study the ergodic properties of a class of measures on for which, where is a collection of matrices. The measure is called a matrix Gibbs state. In particular, we give a sufficient condition for a matrix Gibbs state to have the weak Bernoulli property. We employ a number of techniques to understand these measures, including a novel approach based on Perron-Frobenius theory. We find that when is an even integer the ergodic properties of are readily deduced from finite-dimensional Perron-Frobenius theory. We then consider an extension of this method to 0]]> using operators on an infinite- dimensional space. Finally, we use a general result of Bradley to prove the main theorem.