关于 Wigner 矩阵和协方差矩阵特征值计数函数的中心极限定理
概率论
2011-02-18 v3
摘要
本文介绍了 Wigner 矩阵特征值计数函数的一些中心极限定理，其形式是对 Gustavsson 和 O'Rourke 关于高斯矩阵半圆律谱内部特征值极限行为的结果进行适当平移。然后，通过陶哲轩和武鸿熙的四矩定理，将这些定理推广到 Wigner 矩阵的大族。类似的结果也针对协方差矩阵进行了推导。
引用
@article{arxiv.1011.4042,
title = {On the Central Limit Theorem for the Eigenvalue Counting Function of Wigner and Covariance matrices},
author = {Sandrine Dallaporta},
journal= {arXiv preprint arXiv:1011.4042},
year = {2011}
}
备注
This paper has been withdrawn because a better result has been achieved and is contained in the following note arXiv:1101.2553, which was written with Van Vu