  Numerical simulations of the two-point eigenvalue correlation and cluster
functions of the Gaussian unitary ensemble (GUE) are carried out directly from
their definitions in terms of deltas functions. The simulations are compared
with analytical results which follow from three analytical formulas for the
two-point GUE cluster function: (i) Wigner's exact formula in terms of Hermite
polynomials, (ii) Brezin and Zee's approximate formula which is valid for
points with small enough separations and (iii) French, Mello and Pandey's
approximate formula which is valid on average for points with large enough
separations. It is found that the oscillations present in formulas (i) and (ii)
are reproduced by the numerical simulations if the width of the function used
to represent the delta function is small enough and that the non-oscillating
behaviour of formula (iii) is approached as the width is increased.
