Density of states for high landau levels and random potential

The density of states of a two-dimensional, non-interacting electron gas under the influence of a strong perpendicular magnetic field and random impurities is examined. In the strong magnetic field the ensemble averaged Green's function can be restricted to a single Landau leveln. Using 1/n as expansion parameter we calculate first order corrections. The results for two models of disorder are compared: white-noise potential and uniformly distributed zero-range scatterers with a Lorentzian distribution of strength.