05-101 F. Germinet, A. Klein

New characterizations of the region of complete localization for random Schrodinger operators (406K, pdf) Mar 8, 05

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Abstract. e study the region of complete localization in a class of random operators which includes random Schr\"odinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding model. We establish new characterizations or criteria for this region of complete localization, given either by the decay of eigenfunction correlations or by the decay of Fermi projections. Using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity, a new result for multi-dimensional random operators on the continuum.

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