Kotani theory for one dimensional stochastic Jacobi matrices |
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Authors: | Barry Simon |
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Institution: | 1. Departments of Mathematics and Physics, California Institute of Technology, 91125, Pasadena, CA, USA
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Abstract: | We consider families of operators,H ω, on ?2 given by (H ω u)(n)=u(n+1)+u(n?1)+V ω(n)u(n), whereV ω is a stationary bounded ergodic sequence. We prove analogs of Kotani's results, including that for a.e. ω,σac(H ω) is the essential closure of the set ofE where γ(E) the Lyaponov index, vanishes and the result that ifV ω is non-deterministic, then σac is empty. |
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