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Exact results are obtained on the localization of eigenstates in one-dimensional infinite disordered systems with diagonal and off-diagonal randomness. A Furstenberg-type theorem is established for the product of matrices associated with a multi-Markov-chain. As a result, Matsuda and Ishii's theory is generalized to examine the systems with both randomnesses. Harmonic chains, tightly binding electronic systems and Heisenberg-Mattis model are considered as typical examples.
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Masaki Gôda (1982) studied this question.
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