Random-matrix theory of impurity band tails

We revisit the well-known problem of density of states in the impurity band tails using a random-matrix theory approach. As a model for the system, we consider a ''tridiagonal'' random matrix with diagonal elements taken to be independent and Gaussian distributed. We solve the model in one dimension using a recursive method in the large-N (number of sites) limit. We obtain an analytical expression that agrees with Lifshitz-Halperin-Lax results for energy dependence of the density of states as a stretched exponent of E(3/2) in the asymptotic regime.