A Difference Equation Arising from the Trigonometric Moment Problem Having Random Reflection Coefficients - An Operator Theoretic Approach

Operators associated with polynomials orthogonal on the unit circle and their doubly infinite analogs are considered. We assume that the elements in the operators are obtained from a stationary stochastic process and we investigate the properties of the spectrum of these operators. Lyapunov exponents are introduced and we examine their relationship with the absolutely continuous components of the spectrum of the above operators.