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 $\ell^2(\mathbb Z^d)$. 
Denis Borisov, Francisco Hoecker-Escuti, Ivan Veseli\'c
math-ph math.MP