Abstract
A numerical Monte Carlo technique is used to calculate the density of states and the conductivity of model binary alloys. The strength of the method is its ability to accurately account for local atomic configurations while avoiding explicit many-atom-cluster calculations. Another important feature of the method is its ability to describe Anderson localisation. Results for densities of states and conductivities are presented for various model systems and compared with the corresponding results of an effective-medium theory. A new result of the theory is the occurrence of multiple mobility edges separating regions of Anderson localised states inside the minority band.