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Nonperturbative localization

Svetlana Ya. Jitomirskaya
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Abstract

Study of fine spectral properties of quasiperiodic and similar discrete Schrödinger operators involves dealing with problems caused by small denominators, and until recently was only possible using perturbative methods, requiring certain small parameters and complicated KAM-type schemes. We review the recently developed nonperturbative methods for such study which lead to stronger results and are significantly simpler. Numerous applications mainly due to J. Bourgain, M. Goldstein, W. Schlag, and the author are also discussed.

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Svetlana Ya. Jitomirskaya. 2003-04-28. Nonperturbative localization. https://arxiv.org/abs/math-ph/0304044

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