Localization in general one dimensional random systems, I. Jacobi matrices

We consider random discrete Schroedinger operators in a strip with a potential Vsub(ω)(n,α) (n a label in Z and α a finite label ''across'' the strip) and Vsub(ω) an ergodic process. We prove that H0+Vsub(ω) has only point spectrum with probability one under two assumptions: (1) the conditional distribution of [Vsub(ω)(n,α)]sub(n=0,1;allα) conditioned on [Vsub(ω)]sub(nnot equal0;allα) has an absolutely continuous component with positive probability. (2) For a.e. E, no Lyaponov exponent is zero. (orig.)