Random Magnetic Impurities and the Landau Problem

The 2-dimensional density of states of an electron is studied for a Poissonian random distribution of point vortices carrying $\alpha$ flux in unit of the quantum of flux. It is shown that, for any given density of impurities, there is a transition, when $\alpha\simeq 0.3-0.4$, from an "almost free" density of state -with only a depletion of states at the bottom of the spectrum characterized by a Lifschitz tail- to a Landau density of state with sharp Landau level oscillations. Several evidences and arguments for this transition -numerical and analytical- are presented.