Sharp estimates for the integrated density of states in Anderson tight-binding models

  title={Sharp estimates for the integrated density of states in Anderson tight-binding models},
  author={Perceval Desforges and Svitlana Mayboroda and Shiwen Zhang and Guy David and Douglas N. Arnold and Wei Wang and Marcel Filoche},
  journal={Physical Review A},
Recent work [1] has proved the existence of bounds from above and below for the Integrated Density of States (IDOS) of the Schrodinger operator throughout the spectrum, called the \emph{Landscape Law}. These bounds involve dimensional constants whose optimal values are yet to be determined. Here, we investigate the accuracy of the Landscape Law in 1D and 2D tight-binding Anderson models, with binary or uniform random distributions. We show, in particular, that in 1D, the IDOS can be… 

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