发表机构
The University of Hong Kong; Fudan University（香港大学; 复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立随机酉系综极端特征值分布的Edgeworth展开，揭示修正项的普适结构，并给出最大和最小特征值分布的完全展开。
AI 中文摘要
本文在谱边缘处建立了两类随机酉系综极端特征值分布的Edgeworth展开，并揭示了修正项的某些普适结构。更确切地说，我们证明了高斯型酉系综和拉盖尔型酉系综的关联核分别在软边缘和硬边缘处具有完全展开。修正项的系数由Airy函数或第一类Bessel函数及其导数的有限和给出，并带有多项式系数。通过将核展开提升到相关的Fredholm行列式，我们进一步获得了高斯型酉系综最大特征值分布和拉盖尔型酉系综最小特征值分布的完全展开。此外，其中的第一修正项涉及首项的导数。
英文摘要
In this paper, we establish Edgeworth expansions of extreme eigenvalue distributions for two types random unitary ensembles at the spectral edges and reveal certain universal structures for the correction terms. More precisely, we show the correlation kernels for the Gaussian-type unitary ensembles and Laguerre-type unitary ensembles admit full expansions at the soft edge and the hard edge, respectively. The coefficients of the correction terms are given by finite sums of Airy function or the Bessel functions of the first kind and their derivatives with polynomial coefficients. By lifting the kernel expansion to the associated Fredholm determinant, we further obtain full expansions for the largest eigenvalue distribu- tion of the Gaussian-type unitary ensembles and the smallest eigenvalue distribution of the Laguerre-type unitary ensembles. In addition, the first correction term therein involves the derivatives of the leading term.
Comments42 pages
