Moment analysis for localization in random Schrödinger operators

@article{Aizenman2005MomentAF,
  title={Moment analysis for localization in random Schr{\"o}dinger operators},
  author={Michael Aizenman and Alexander Elgart and Serguei Naboko and Jeffrey Schenker and Gunter Stolz},
  journal={Inventiones mathematicae},
  year={2005},
  volume={163},
  pages={343-413}
}
We study localization effects of disorder on the spectral and dynamical properties of Schrödinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the analysis of fractional moments of the resolvent, which are finite due to the resonance-diffusing effects of the disorder. The main difficulty which has up to now prevented an extension of this method… 

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