EXACT RESULTS ON LANDAU-LEVEL BROADENING

For an electron in the plane subjected to a perpendicular constant magnetic field and a homogeneous random potential we investigate the averaged density of states restricted to an arbitrary Landau level. We calculate the exact width for an arbitrary random potential. For general Gaussian random potentials we prove the existence of Gaussian tails and determine the decay constants. Furthermore, we derive Jensen-type lower and upper bounds to expectation values of convex functions with respect to the restricted density of states. Using similar bounds we estimate the effect of Landau-level mixing.