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In this work we consider the Anderson model on $\ell^2(\mathbb{Z}^d)$ whenthe single site distribution (SSD) is given by $\mu_1 * \mu_2$, where $\mu_1$is the Cauchy distribution and $\mu_2$ is any probability measure. For thismodel we prove that the integrated density of states (IDS) is infinitelydifferentiable irrespective of the disorder strength. Also, we investigate thelocal eigenvalue statistics of this model in $d\ge 2$, without any assumptionon the localization property.

Smoothness of integrated density of states and level statistics of the  Anderson model when single site distribution is convolution with the Cauchy  distribution