  This paper centers on the limit eigenvalue distribution for random
Vandermonde matrices with unit magnitude complex entries. The phases of the
entries are chosen independently and identically distributed from the interval
$[-\pi,\pi]$. Various types of distribution for the phase are considered and we
establish the existence of the empirical eigenvalue distribution in the large
matrix limit on a wide range of cases. The rate of growth of the maximum
eigenvalue is examined and shown to be no greater than $O(\log N)$ and no
slower than $O(\log N/\log\log N)$ where $N$ is the dimension of the matrix.
Additional results include the existence of the capacity of the Vandermonde
channel (limit integral for the expected log determinant).
