Fr\'ed\'eric Klopp.
A low concentration asymptotic expansion for the density of states of a random Schr\"odinger operator with Poisson disorder.
(65K, AMSTeX)
ABSTRACT. In this paper, we study the density of states of a random Schr\"odinger operator of the form $H_\omega=-\Delta+V_\omega$
where $V_\omega$ is a Poisson potential (i.e a Poisson random field) of concentration $\mu$.
We show that $N_\mu(d\lambda)$, the density of states of $H_\omega$, admits an asymptotic expansion in $\mu$ when $\mu\to0$.
Then, we use this expansion to deduce the behaviour of the integrated density of states of $H_\omega$ in the energy interval $(-\infty,0)$ when
$\mu$ goes to 0.