Universality of correlations of levels with discrete statistics

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 p roblem arises in sums over representations (Young tableaux) of GL(N) in var ious matrix problems and in the study of statistics of partitions for the p ermutation group. The model is generalized to include an external source an d its correlators are found in closed form for any N. We reproduce the dens ity of levels in the large N and double scaling limits and the universal co rrelation functions in Dyson's short-distance scaling limit. We also study the statistics of small levels.