Jean-Michel Combes, Francois Germinet, Peter Hislop
On the quantization of Hall currents in presence of disorder
(309K, .pdf)

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.