Discontinuities of the integrated density of states for random operators   on Delone sets
  Despite all the analogies with "usual random" models, tight binding operators for quasicrystals exhibit a feature which clearly distinguishes them from the former: the integrated density of states may be discontinuous. This phenomenon is identified as a local effect, due to occurrence of eigenfunctions with bounded support. 
Steffen Klassert, Daniel Lenz and Peter Stollmann