 05197 Domingos H. U. Marchetti, Walter F. Wreszinski, Leonardo F. Guidi, Renato M. Angelo
 OffDiagonal Jacobi Matrices as a Model for a Spectral Transition of Anderson Type
(1319K, Postscript)
May 31, 05

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Abstract. We introduce a class of Jacobi matrices which model a deterministic (sparse) disorder in the sense that the perturbation of the Laplacean consists of a(direct) sum of fixed offdiagonal two by two matrices placed at sites whose distances from one another grow exponentially. We prove that the spectrum is the set [2,2]. For "small coupling" there is (dense) pure point spectrum and for "large coupling" the support of the singular continuous spectral measure contains a set of positive Lebesgue measure, if the Pr fer angles are uniformly distributed. There is compelling numerical evidence for the latter property, which is briefly discussed.
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