On localization for the Schr\"odinger operator with a Poisson random   potential
  We prove exponential localization for the Schr\"odinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson densities. In addition, we obtain dynamical localization and finite multiplicity of the eigenvalues. 
Francois Germinet, Peter Hislop, Abel Klein