  Statistics of the local density of states in the two-dimensional
Falicov-Kimball model with local disorder is studied by employing the
statistical dynamical mean-field theory. Within the theory the local density of
states and its distributions are calculated through stochastic self-consistent
equations. The most probable value of the local density of states is used to
monitor the metal-insulator transition driven by correlation and disorder.
Nonvanishing of the most probable value of the local density of states at the
Fermi energy indicates the existence of extended states in the two-dimensional
disordered interacting system. It is also found that the most probable value of
the local density of states exhibits a discontinuity when the system crosses
from extended states to the Anderson localization. A phase diagram is also
presented.
