Equality of the density of states in a wide class of tight-binding Lorentzian random models

Abstract

We prove directly the equality of the density of states in a wide class of tight-binding Lorentzian random models, including the Lloyd model, the $tan(2\mathrm{}\pi \alpha n+\theta )$ model of Grempel, Fishman, and Prange, and a model with potential $\Sigma i^{}{\psi }_{i}tan\left(2\mathrm{}\pi {\alpha }_{i}n\right)$, where $\Sigma i^{}{\psi }_i=1\mathrm{}$ and the ${\alpha }_i$ are rationally independent.