GUE和LUE的最大Eigenvalue分布函数的Edgeworth展开
Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE and LUE
摘要：
我们推导了Hermite和Laguerre核在有限n高斯酉系综（GUEn）和有限n Laguerre酉系综（LUEn）谱边缘的展开式。利用这些大的n核展开，我们证明了一个Edgeworth型定理的最大特征值分布函数的GUEn和LUEn。在我们的Edgeworth展开式中，校正项用出现在首项中的相同Painleve II函数表示，即在Tracy-Widom分布中。最后，我们简要讨论了这些结果的普遍性。
英文摘要：
We derive expansions of the Hermite and Laguerre kernels at the edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the finite n Laguerre Unitary Ensem- ble (LUEn), respectively. Using these large n kernel expansions, we prove an Edgeworth type theorem for the largest eigenvalue distribution function of GUEn and LUEn. In our Edgeworth expansion, the correction terms are expressed in terms of the same Painleve II function appearing in the leading term, i.e. in the Tracy-Widom distribution. We conclude with a brief discussion of the universality of these results.
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