Eigenfunction Statistics for Anderson Model with H\"{o}lder continuous single site Potential

Abstract

We consider random Schr\"{o}dinger operators on $\ell^2(\mathbb{Z}^d)$ when the distribution of single site potentials is $\alpha$-H\"{o}lder continuous ($0<\alpha\leq 1$). In localized regime we study the distribution of eigenfunctions simultaneously in space and energy. In a certain scaling limit we prove limits point are Poisson.