Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case

• Main Authors: Pan, Guangming, Wang, Shaochen, Zhou, Wang
• 其他作者: School of Physical and Mathematical Sciences
• 格式: Article
• 語言: English
• 出版: 2017
• 主題: Wigner matrix; Linear eigenvalue statistic
• 在線閱讀: https://hdl.handle.net/10356/85600; http://hdl.handle.net/10220/43758

In this note, we consider the fluctuation theorem for X(n)fn := ∑f(λi)I(λi≥θn), where λi, i=1,…,n are eigenvalues from a Wigner matrix and θn→2−. We prove that in the edge case X(n)fn behaves like the counting function of Wigner matrix. Our results can be viewed as a complement of Bao et al. (J Stat...