  The influence of electron-electron (e-e) interactions on the transmission
through a quantum dot is investigated numerically for the Coulomb blockade
regime. For vanishing magnetic fields, the conductance peak height statistics
is found to be independent of the interactions strength. It is identical to the
statistics predicted by constant interaction single electron random matrix
theory and agrees well with recent experiments. However, in contrast to these
random matrix theories, our calculations reproduces the reduced sensitivity to
magnetic flux observed in many experiments. The relevant physics is traced to
the short range Coulomb correlations providing thus a unified explanation for
the transmission statistics as well as for the large conductance peak spacing
fluctuations observed in other experiments.
