W. Kirsch and F. Klopp
The band-edge behavior of the density of surfacic states
(514K, PDF)
ABSTRACT. This paper is devoted to the asymptotics of the density of surfacic
states near the spectral edges for a discrete surfacic Anderson
model. Two types of spectral edges have to be considered :
fluctuating edges and stable edges. Each type has its own type of
asymptotics. In the case of fluctuating edges, one obtains Lifshitz
tails the parameters of which are given by the initial operator
suitably ``reduced'' to the surface. For stable edges, the surface
density of states behaves like the surface density of states of a
constant (equal to the expectation of the random potential) surface
potential. Among the tools used to establish this are the
asymptotics of the surface density of states for constant surface
potentials.