Support theorems for random Schrödinger operators (Q1063326)

In the multi-dimensional case it is shown that the increase of the topological support of the probability measure describing the randomness of potentials implies the increase of the spectrum. In the one- dimensional case the converse statement for the absolutely continuous spectrum is valid. Especially the spectrum (in general dimension) and the absolutely continuous spectrum (in one-dimension) are determined only by the topological support of the random potentials.