We consider the random operator: -d/mω(dx)d+/dx+qω(x), where mω(dx) and qω(x) are a stationary ergodic random measure and a random function respectively. To this general case, we extend Kotani's theorem which asserts that the absolutely continuous spectrum is completely determined by the Ljapounov indices. Our framework includes the case of stochastic Jacobi matrices treated by Simon.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics