  Under certain conditions on k we calculate the limit distribution of the k:th
largest eigenvalue, x_k, of the Gaussian Unitary Ensemble (GUE). More
specifically, if n is the dimension of a random matrix from the GUE and k is
such that both k and n-k tends to infinity as n tends to infinity then x_k is
normally distributed in the limit. We also consider the joint limit
distribution of x_k_1 < ... < x_k_m where we require that k_1, k_{i+1}-k_i and
n-k_m, i=1..m-1, tends to infinity with n. The result is an m-dimensional
Normal Distribution.
