  We study the statistics of a system of N random levels with integer values,
in the presence of a logarithmic repulsive potential of Dyson type. This
probleme arises in sums over representations (Young tableaux) of GL(N) in
various matrix problems and in the study of statistics of partitions for the
permutation group. The model is generalized to include an external source and
its correlators are found in closed form for any N. We reproduce the density of
levels in the large N and double scaling limits and the universal correlation
functions in Dyson's short-distance scaling limit. We also study the statistics
of small levels.
