Localization in general one dimensional random systems. I: Jacobi matrices
We consider random discrete Schrödinger operators in a strip with a potential \(V_{\omega}(n,\alpha)\) (n a label in \({\mathbb{Z}}\) and \(\alpha\) a finite label ''across'' the strip) and \(V_{\omega}\) an ergodic process. We prove that \(H_ 0+V_{\omega}\) has only point spectrum with probability one under two assumptions: (1) The conditional distribution of \(\{V_{\omega}(n,\alpha)\}_{n=0,1;all\quad \alpha}\) conditioned on \(\{V_{\omega}\}_{n\neq 0,1;all\quad \alpha}\) has an absolutely continuous component with positive probability. (2) For a.e. E, no Lyapunov exponent is zero.
scientific article; zbMATH DE number 3976028
scientific article