Some Estimates Regarding Integrated density of States for Random Schrödinger Operator with decaying Random Potentials (1501.05055v2)

Published 21 Jan 2015 in math.SP

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 $a_n\simeq|n|^{{-\alpha}~~\alpha>0$.}