Hölder continuity of the integrated density of states for some random operators at all energies

We prove that the integrated density of states of random Schrödinger operators with Anderson-type potentials on L²(ℝ^d), for d ≥ 1, is locally Hölder continuous at all energies for d ≥ 2, and Lipschitz continuous at all energies for d = 1. The single-site potential u must be nonnegative and compactly supported, and the distribution of the random variable must be absolutely continuous with a bounded, compactly supported density. We also prove continuity of the integrated density of states at all energies for random Anderson-type perturbations of the Landau Hamiltonian in two dimensions, and Hölder continuity under an additional rational flux condition.