Abstract
We consider families of operators,H ω, on ℓ2 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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Communicated by T. Spencer
Research partially supported by USNSF under Grant MCS-81-20833
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Simon, B. Kotani theory for one dimensional stochastic Jacobi matrices. Commun.Math. Phys. 89, 227–234 (1983). https://doi.org/10.1007/BF01211829
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DOI: https://doi.org/10.1007/BF01211829