The Size of Localized States Near the Mobility Edge

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Abstract
The "mobility edge" is the critical point at which a transition from localized to extended character of the eigenfunctions occurs in the random lattice problem. We study the behavior of the eigenfunctions as this critical point is approached, and produce arguments that suggest that they fall off, on the average, as exp(-alpha)R with range R, and that alpha alpha [E - E(c)](0.6).