  Taking into account that a proper description of disordered systems should
focus on distribution functions, the authors develop a powerful numerical
scheme for the determination of the probability distribution of the local
density of states (LDOS), which is based on a Chebyshev expansion with kernel
polynomial refinement and allows the study of large finite clusters (up to
$100^3$). For the three-dimensional Anderson model it is demonstrated that the
distribution of the LDOS shows a significant change at the disorder induced
delocalisation-localisation transition. Consequently, the so-called typical
density of states, defined as the geometric mean of the LDOS, emerges as a
natural order parameter. The calculation of the phase diagram of the Anderson
model proves the efficiency and reliability of the proposed approach in
comparison to other localisation criteria, which rely, e.g., on the decay of
the wavefunction or the inverse participation number.

Disordered Systems and Neural Networks