  Analytical expressions for width and conductance peak distributions for
quantum dots with multi-channel leads in the Coulomb blockade regime are
presented for both limits of conserved and broken time-reversal symmetry. The
results are valid for any number of non-equivalent and correlated channels, and
the distributions are expressed in terms of the channel correlation matrix $M$
in each lead. The matrix $M$ is also given in closed form. A chaotic billiard
is used as a model to test numerically the theoretical predictions.
