Stochastic Schrödinger operators and Jacobi matrices on the strip (Q1110193)

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions taking values in \({\mathbb{C}}^{\ell}\) so that there are \(2\ell\) Lyapunov exponents \(\gamma_ 1\geq...\geq \gamma_{\ell}\geq 0\geq \gamma_{\ell +1}\geq...\geq \gamma_{2\ell}=-\gamma_ 1\). Our results include the facts that if \(\gamma_ 1=0\) on a set of positive measure then V is deterministic, and one that says that \(\{\) \(E| exactly\) 2j \(\gamma\) 's are zero\(\}\) is the essential support of the a.c. spectrum of multiplicity 2j.