  Recent theoretical studies of chaotic scattering have encounted ensembles of
random matrices in which the eigenvalue probability density function contains a
one-body factor with an exponent proportional to the number of eigenvalues. Two
such ensembles have been encounted: an ensemble of unitary matrices specified
by the so-called Poisson kernel, and the Laguerre ensemble of positive definite
matrices. Here we consider various properties of these ensembles. Jack
polynomial theory is used to prove a reproducing property of the Poisson
kernel, and a certain unimodular mapping is used to demonstrate that the
variance of a linear statistic is the same as in the Dyson circular ensemble.
For the Laguerre ensemble, the scaled global density is calculated exactly for
all even values of the parameter $\beta$, while for $\beta = 2$ (random
matrices with unitary symmetry), the neighbourhood of the smallest eigenvalue
is shown to be in the soft edge universality class.
