Understanding the Random Displacement Model: From Ground-State   Properties to Localization
  We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model. 
Fr\'ed\'eric Klopp, Michael Loss, Shu Nakamura and G\"unter Stolz
math-ph math.MP math.SP