 03296 Domingos H. U. Marchetti, Walter F. Wreszinski
 OffDiagonal Jacobi Matrices as a Model for Spectral Transition
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Jun 23, 03

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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] and there is a
transition from (singular) continuous spectrum, for small "coupling",
to (dense) pure point spectrum, for large "coupling", if the
corresponding Pr\"{u}fer angles are uniformly distributed (u.d.).
We then prove that the latter sequence is u.d. almost everywhere for
a certain range of parameters which is a result of independent interest.
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