A Note on the Analyticity of Density of States

We consider the $d$-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We employ the random walk expansion of resolvents and a simple complex function theory trick. In particular, we discuss the uniform distribution case, and we obtain a sharper result using more precise computations. The method can be also applied to prove the analyticity of the correlation functions.