J. M. Combes, P. D. Hislop, F. Klopp, G. Raikov
Global continuity of the integrated density of states for random Landau Hamiltonians
(80K, LaTex 2e)
ABSTRACT. We prove that the integrated density of states (IDS)
for the randomly perturbed Landau Hamiltonian is H\"older continuous at all energies with any H\"older exponent $0 < q < 1$.
The random Anderson-type potential is constructed with a nonnegative, compactly supported single-site potential $u$. The distribution of the {\it iid} random variables must be absolutely continuous with
a bounded, compactly supported density.
This extends a previous result \cite{[CHK1]}
that was restricted to magnetic fields having rational
flux through the unit square. Furthermore, we prove that the IDS is
H\"older continuous as a function of the nonzero
magnetic field strength, and that the density of states is in $L^p_{loc} ( \R)$, for any $1 \leq p < \infty$.