Some Estimates Regarding Integrated density of States for Random Schr\"{o}dinger Operator with decaying Random Potentials

Abstract

We investigate some bounds for the density of states in the pure point regime for the random Schr\"{o}dinger operators $H^{\omega}=-\Delta+\displaystyle\sum_{n\in\mathbb{Z}^d}a_nq_n(\omega)$, acting on $\ell^2(\mathbb{Z}^d)$, where $\{q_n\}$ are iid random variables and $a_n\simeq|n|^{-\alpha}~~\alpha>0$.