Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case

• Main Authors: Pan, Guangming, Wang, Shaochen, Zhou, Wang
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2017
• Subjects: Wigner matrix; Linear eigenvalue statistic
• Online Access: https://hdl.handle.net/10356/85600; http://hdl.handle.net/10220/43758
• Institution: Nanyang Technological University

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...