Prefer a chat interface with context about you and your work?
Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory
In this paper, we consider the asymptotic behavior of 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 VarXfn(n)→∞, the Berry-Esseen (BE) bound and Cramér type moderate deviation principle (MDP) for Xfn(n) are obtained by using the method of cumulants. …