  In this paper we consider an asymptotic question in the theory of the
Gaussian Unitary Ensemble of random matrices. In the bulk scaling limit, the
probability that there are no eigenvalues in the interval (0,2s) is given by
P_s=det(I-K_s), where K_s is the trace-class operator with kernel
K_s(x,y)={sin(x-y)}/{\pi(x-y)} acting on L^2(0,2s). We are interested
particularly in the behavior of P_s as s tends to infinity...
