Duke Mathematical Journal
- Duke Math. J.
- Volume 146, Number 2 (2009), 331-360.
Lifshitz tails and localization in the three-dimensional Anderson model
Consider the three-dimensional Anderson model with a zero mean and bounded independent, identically distributed random potential. Let be the coupling constant measuring the strength of the disorder, and let be the self-energy of the model at energy . For any and sufficiently small , we derive almost-sure localization in the band . In this energy region, we show that the typical correlation length behaves roughly as , completing the argument outlined in the preprint of T. Spencer 
Duke Math. J., Volume 146, Number 2 (2009), 331-360.
First available in Project Euclid: 5 January 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.) 81T15: Perturbative methods of renormalization
Secondary: 47B80: Random operators [See also 47H40, 60H25] 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis 81T18: Feynman diagrams
Elgart, Alexander. Lifshitz tails and localization in the three-dimensional Anderson model. Duke Math. J. 146 (2009), no. 2, 331--360. doi:10.1215/00127094-2008-068. https://projecteuclid.org/euclid.dmj/1231170943