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Exact local distribution of the absolutely continuous spectral measure
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abstract
It is well-established that the spectral measure for one-frequency Schr\"odinger operators with Diophantine frequencies exhibits optimal $1/2$-H\"older continuity within the absolutely continuous spectrum. This study extends these findings by precisely characterizing the local distribution of the spectral measure for dense small potentials, including a notable result for any subcritical almost Mathieu operators. Additionally, we investigate the stratified H\"older continuity of the spectral measure at subcritical energies.
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Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition
Packing and multifractal dimensions of almost Mathieu spectral measures have upper bounds that vanish at the arithmetic transition where ln lambda equals beta.
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