Anderson localization and Lifshits tails for random surface potentials

We consider Schrödinger operators on L²(ℝ^d) with a random potential concentrated near the surface ℝ^d1 × {0} ⊂ ℝ^d. We prove that the integrated density of states of such operators exhibits Lifshits tails near the bottom of the spectrum. From this and the multiscale analysis by Boutet de Monvel and Stollmann [Arch. Math. 80 (2003) 87-97] we infer Anderson localization (pure point spectrum and dynamical localization) for low energies. Our proof of Lifshits tails relies on spectral properties of Schrödinger operators with partially periodic potentials. In particular, we show that the lowest energy band of such operators is parabolic.