Expansion of the almost sure spectrum in the weak disorder regime

The spectrum of random ergodic Schr"odinger-type operators is almost surely a deterministic subset of the real line. The random operator can be considered as a perturbation of a periodic one. As soon as the disorder is switched on via a global coupling constant, the spectrum expands. We estimate how much the spectrum expands at its bottom for operators on ${\mathrm{\ell }}^2({\mathbb{Z}}^d)$.