  The ensemble $\CUE^{(q)}$ of truncated random unitary matrices is a
deformation of the usual Circular Unitary Ensemble depending on a discrete
non-negative parameter $q.$ $\CUE^{(q)}$ is an exactly solved model of random
contraction matrices originally introduced in the context of scattering theory.
In this article, we exhibit a connection between $\CUE^{(q)}$ and Fisher's
random-turns vicious walker model from statistical mechanics. In particular, we
show that the moment generating function of the trace of a random matrix from
$\CUE^{(q)}$ is a generating series for the partition function of Fisher's
model, when the walkers are assumed to represent mutually attracting particles.
