  We studied several aspects of the Mott metal-insulator transition in the
disordered case. The model on which we based our analysis is the disordered
Hubbard model, which is the simplest model capable of capturing the Mott
metal-insulator transition. We investigated this model through the Statistical
Dynamical Mean-Field Theory (statDMFT). This theory is a natural extension of
the Dynamical Mean-Field Theory (DMFT), which has been used with relative
success in the last several years with the purpose of describing the Mott
transition in the clean case. As is the case for the latter theory, the
statDMFT incorporates the electronic correlation effects only in their local
manifestations. Disorder, on the other hand, is treated in such a way as to
incorporate Anderson localization effects. With this technique, we analyzed the
disordered two-dimensional Mott transition, using Quantum Monte Carlo to solve
the associated single-impurity problems. We found spinodal lines at which the
metal and insulator cease to be meta-stable. We also studied spatial
fluctuations of local quantities, such as the self-energy and the local Green's
function, and showed the appearance of metallic regions within the insulator
and vice-versa. We carried out an analysis of finite-size effects and showed
that, in agreement with the theorems of Imry and Ma, the first-order transition
is smeared in the thermodynamic limit. We analyzed transport properties by
means of a mapping to a random classical resistor network and calculated both
the average current and its distribution across the metal-insulator transition.
