Localization near fluctuation boundaries via fractional moments and applications

We present a new, short, self-contained proof of localization properties of multi-dimensional continuum random Schr\"odinger operators in the fluctuation boundary regime. Our method is based on the recent extension of the fractional moment method to continuum models in by Aizenman et al, but does not require the random potential to satisfy a covering condition. Applications to random surface potentials and potentials with random displacements are included.