Abstract
We review recent results of two of the authors concerning the quantization of Hall currents, in particular a general quantization formula for the difference of edge Hall conductances in semi-infinite samples with and without a confining wall. We then study the case where the Fermi energy is located in a region of localized states and discuss new regularizations. We also sketch the proof of localization for 2D-models with constant magnetic field with random potential located in a half-plane in two different situations: (1) with a zero potential in the other half plane and for energies away from the Landau levels and (2) with a confining potential in the other half plane and on an interval of energies that covers an arbitrary number of Landau levels.
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