  In previous work we have found a regime in ballistic quantum dots where
interelectron interactions can be treated asymptotically exactly as the
Thouless number $g$ of the dot becomes very large. However, this work depends
on some assumptions concerning the renormalization group and various properties
of the dot obeying Random Matrix Theory predictions at scales of the order of
the Thouless energy. In this work we test the validity of those assumptions by
considering a particular ballistic dot, the Robnik-Berry billiard, numerically.
We find that almost all of our predictions based on the earlier work are borne
out, with the exception of fluctuations of certain matrix elements of
interaction operators. We conclude that, at least in the Robnik-Berry billiard,
one can trust the results of our previous work at a qualitative and
semi-quantitative level.
