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We present a short, new, self-contained proof of localization properties of multi-dimensional continuum random Schödinger operators in the fluctuation boundary regime. Our method is based on the recent extension of the fractional moment method to continuum models in [2] but does not require the random potential to satisfy a covering condition. Applications to random surface potentials and potentials with random displacements are included.

Localization near fluctuation boundaries via fractional moments and applications