Internal edges:

The known results depend very much on dimension, and on whether 
the single site potential is short or long range.

E.g., in the short range case, in dimension 1, Mezincescu proved Lifshitz tails 
at all band under quite general assumptions.

The periodic density of states:
 
Let  be the integrated density of states for.

Under our assumptions, the spectrum of  has a gap below 0 starting at 0. 



The behavior of  will play an important role in the study of Lifshitz tails.

Note : there are almost no general results on the behavior of