Upper bounds on the density of states of single Landau levels broadened byGaussian random potentials

We study a nonrelativistic charged particle on the Euclidean plane R-2 subj ect to a perpendicular constant magnetic field and an R-2-homogeneous rando m potential in the approximation that the corresponding random Landau Hamil tonian on the Hilbert space L-2(R-2) is restricted to the eigenspace of a s ingle but arbitrary Landau level. For a wide class of R-2-homogeneous Gauss ian random potentials we rigorously prove that the associated restricted in tegrated density of states is absolutely continuous with respect to the Leb esgue measure. We construct explicit upper bounds on the resulting derivati ve, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian. (C) 2001 American Institute of Physics.