  In a quantum dot with three leads the transmission matrix t_{12} between two
of these leads is a truncation of a unitary scattering matrix S, which we treat
as random. As the number of channels in the third lead is increased, the
constraints from the symmetry of S become less stringent and t_{12} becomes
closer to a matrix of complex Gaussian random numbers with no constraints. We
consider the distribution of the singular values of t_{12}, which is related to
a number of physical quantities. Changing the number of channels in the third
lead corresponds to increasing the amount of loss in the system (and is
distinct from prior uses of a third lead to model dephasing).
