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 ${\xi }_{L,\lambda }^{\omega }$ associated with eigenvalues of $H_{{\Lambda }_L}^{\omega }$, the retriction of $H^{\omega }$ to the finite cube ${\Lambda }_L$. Our result is that the weak limit points of $\{{\xi }_{L,\lambda }^{\omega }\}$ are poisson point processes as $L\to \infty$.

arXiv commentThis paper has been withdrawn by the author due to a crucial technical error