Abstract
For a class of random Schrödinger operators in L2(Rd▪ where qj are continuous independent identically distributed bounded random variables and f has a power decay and defined sign, in any energy interval the singular continuous spectrum is either empty or with positive Lebesgue measure. As a consequence, the proof of localization for a class of random but deterministic one-dimensional operators is shifted to showing that the singular continuous spectrum has null Lebesgue measure.
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