Periodic Schrödinger operator:

On consider the -periodic Schrödinger operator



with  a bounded real valued potential. Let  be its spectrum.

Random perturbations:

The continuous Anderson (or alloy type) model is the random Schrödinger operator



where  is a potential,  and  are i. i. d. random variables.

We assume that they satisfy
 is non-negative ad not identically vanishing.
It decays sufficiently fast for the sum in (1) to converge.
The   are bounded and their support is the interval