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

Numerical Simulation of GUE Two-Point Correlation and Cluster Functions