Spectral statistic for decaying random potentials

Abstract

We consider Anderson model $H^{\omega}=-\Delta+V^{\omega}$ on $\ell^2(\mathbb{Z}^d)$ with decaying random potential. We study the point process $\xi^{\omega}_{L,\lambda}$ associated with eigenvalues of $H^{\omega}_{\Lambda_L}$, the retriction of $H^{\omega}$ to the finite cube $\Lambda_L$. Our result is that the weak limit points of $\{\xi^{\omega}_{L,\lambda}\}$ are poisson point processes as $L\to\infty$.