03-272 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) Jun 10, 03

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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 $1 \leq p < \infty$.

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