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.

中文翻译：

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GUE两点相关和聚类函数的数值模拟

高斯幺正系综 (GUE) 的两点特征值相关和聚类函数的数值模拟直接根据它们在 deltas 函数方面的定义进行。将模拟结果与根据两点 GUE 聚类函数的三个分析公式得出的分析结果进行比较：(i) 用 Hermite 多项式表示的 Wigner 精确公式，(ii) Brezin 和 Zee 的近似公式，对于足够小的点有效间隔和 (iii) French、Mello 和 Pandey 的近似公式，该公式对于间隔足够大的点平均有效。