Abstract: The 2D Schroedinger operator with constant magnetic
field and alloy-type random potential will be considered. It will be shown that
the corresponding IDS is Hoelder continuous at all energies with the exponent
q<1. Some results concerning the continuity of the IDS with respect to the
magnetic field will be also presented. This is a joint work with J.M. Combes,
P. Hislop and F. Klopp.