In a typical situation:


Our main question then is:

how does  behave near 

Note:

the situations at  and  are similar. We will only study the lower band edges.
by shifting the energy and the random variables, one may always 
assume that .
the same question can and has been studied for other random models (Poisson 
model (Pastur, Figotin, Nakao, Sznitman, etc), Gaussian potentials (Leschke et al., 
Ueki,...), random magnetic fields or potentials (Nakamura, Ueki,...), etc).