Band-edge features in disordered systems

Despite the complexity of real disordered materials, the electronic properties often have similar features in dissimilar materials, suggesting the presence of universal features, particularly near band edges. In the present paper, we demonstrate that under certain conditions, including weak disorder, band-edge features are universal for fewer than two dimensions. For higher dimensions, universality remains after a nonuniversal shift of the edge of the unperturbed band. The white-noise model proves very useful in the universality arguments.