Anderson Localization for the Almost Mathieu Equation, III. Semi-Uniform Localization, Continuity of Gaps, and Measure of the Spectrum
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- Jitomirskaya, S. & Last, Y. Comm Math Phys (1998) 195: 1. doi:10.1007/s002200050376
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We show that the almost Mathieu operator, \(\), has semi-uniform (and thus dynamical) localization for λ > 15 and a.e. ω,θ. We also obtain a new estimate on gap continuity (in ω) for this operator with λ > 29 (or λ < 4/29), and use it to prove that the measure of its spectrum is equal to \(\) for λ in this range and all irrational ω's.