95-101 Fr\'ed\'eric Klopp.

An asymptotic expansion for the density of states of a random Schr\"odinger operator with Bernoulli disorder. (52K, AMSTeX) Feb 22, 95

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Abstract. In this paper, we study the density of states of a random Schr\"odinger operators of the form $H(t)=H+\sum_{\gamma\in{\Bbb Z}^d}t_\gamma V_\gamma$. Here $H$ is a periodic Schr\"odinger operator, $V$ is an exponentially decreasing function and $V_\gamma$, its translate by $\gamma$; the random variables $(t_\gamma)_{\gamma\in{\Bbb Z}^d}$ are chosen i. i. d. with the following common Bernoulli probability measure: $t_\gamma=1$ with probability $p$, and $t_\gamma=0$ with probability $1-p$. We show that $N_p(d\lambda)$, the density of states of $H(t)$, has an asymptotic expansion in $p$ when $p\to0$. Then, we use this expansion to deduce the behaviour of the integrated density of states of $H(t)$ in the gaps of $H$ when $p$ goes to 0.

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