  We consider a negative Laplacian in multi-dimensional Euclidean space (or a
multi-dimensional layer) with a weak disorder random perturbation.
  The perturbation consists of a sum of lattice translates of a delta
interaction supported on a compact manifold of co-dimension one and modulated
by coupling constants which are independent identically distributed random
variables times a small disorder parameter.
  We establish that the spectrum of the considered operator is almost surely a
fixed set, characerize its minimum, give an initial length scale estimate and
the Wegner estimate and conclude that there is a small zone of a pure point
spectrum containing the almost sure spectral bottom. The length of this zone is
proportional to the small disorder parameter.
