Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory

• Main Authors: Pan, Guangming, Wang, Shaochen, Zhou, Wang
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2017
• Subjects: Probability Theory; Correlation
• Online Access: https://hdl.handle.net/10356/86704; http://hdl.handle.net/10220/44176
• Institution: Nanyang Technological University

In this paper, we consider the asymptotic behavior of X(n)fn≔∑ni=1fn(xi)Xfn(n)≔∑i=1nfn(xi), where xi,i=1,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that VarX(n)fn→∞VarXfn(n)→∞, the Berry-Esseen (BE) bound and Cramér type moderat...