  We determine the statistical properties of wave functions in disordered
quantum systems by exact diagonalization of one-, two- and quasi-one
dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we
find that the tails of the distribution of wave-function amplitudes are
described by the non-linear sigma-model. In two dimensions, the tails of the
distribution function are consistent with a recent prediction based on a direct
optimal fluctuation method.
