论文标题
线性光谱统计的独立性和Wigner矩阵边缘的点过程
Independence of linear spectral statistics and the point process at the edge of Wigner matrices
论文作者
论文摘要
在当前的论文中，我们考虑了Wigner矩阵，并考虑包含其内部半圆形法的支持的多项式生长的分析功能。我们证明，当Wigner矩阵的条目是亚高斯时，wigner矩阵边缘的函数和点过程对应的线性光谱统计量与点过程是渐进的。证明的主要成分是基于Banerjee [6]的最新论文。本文的结果可以看作是在批量和边缘中找到特征值的关节分布的第一步。
In the current paper we consider a Wigner matrix and consider an analytic function of polynomial growth on a set containing the support of the semicircular law in its interior. We prove that the linear spectral statistics corresponding to the function and the point process at the edge of the Wigner matrix are asymptotically independent when the entries of the Wigner matrix are sub-Gaussian. The main ingredient of the proof is based on a recent paper by Banerjee [6]. The result of this paper can be viewed as a first step to find the joint distribution of eigenvalues in the bulk and the edge.
