  Mathematical analysis of the Anderson localization has been facilitated by
the use of suitable fractional moments of the Green function. Related methods
permit now a readily accessible derivation of a number of physical
manifestations of localization, in regimes of strong disorder, extreme
energies, or weak disorder away from the unperturbed spectrum. The present work
establishes on this basis exponential decay for the modulus of the two--point
function, at all temperatures as well as in the ground state, for a Fermi gas
within the one-particle approximation. Different implications, in particular
for the Integral Quantum Hall Effect, are reviewed.
