Some Estimates Regarding Integrated density of States for Random Schrödinger Operator with decaying Random Potentials

Abstract

We investigate some bounds for the density of states in the pure point regime for the random Schrödinger operators $H^{\omega }=-\Delta +\sum _{n\in {\mathbb{Z}}^d}{a}_n{q}_n(\omega )$, acting on ${\ell }^2({\mathbb{Z}}^d)$, where $\{q_n\}$ are iid random variables and $a_n\simeq |n{|}^{-\alpha }\alpha >0$.