  Despite considerable work on the energy-level and wavefunction statistics of
disordered quantum systems, numerical studies of those statistics relevant for
electron-electron interactions in mesoscopic systems have been lacking. We plug
this gap by using a tight-binding model to study a wide variety of statistics
for the two-dimensional, disordered quantum system in the diffusive regime. Our
results are in good agreement with random matrix theory (or its extensions) for
simple statistics such as the probability distribution of energy levels or
spatial correlation of a wavefunction. However, we see substantial disagreement
in several statistics which involve both integrating over space and different
energy levels, indicating that disordered systems are more complex than
previously thought. These are exactly the quantities relevant to
electron-electron interaction effects in quantum dots; in fact, we apply these
results to the Coulomb blockade, where we find altered spacings between
conductance peaks and wider spin distributions than traditionally expected.
