论文标题
汉克尔矩阵线性特征值统计的非高斯限制
A non-Gaussian limit for linear eigenvalue statistics of Hankel matrices
论文作者
论文摘要
本文着重于具有独立条目的Hankel矩阵的线性特征值统计。利用矩的收敛性，我们表明，hankel矩阵的线性特征值统计奇数单明一度大于或等于三的奇数程度单元，这不会分布到高斯随机变量。该结果与已知的结果，Liu，Sun和Wang（2012），Kumar and Maurya（2022），即均程度单次测试函数的Hankel矩阵的线性特征值统计，其中限制是高斯随机变量。
This article focuses on linear eigenvalue statistics of Hankel matrices with independent entries. Using the convergence of moments we show that the linear eigenvalue statistics of Hankel matrices for odd degree monomials with degree greater than or equal to three does not converge in distribution to a Gaussian random variable. This result is a departure from the known results, Liu, Sun and Wang (2012), Kumar and Maurya (2022), of linear eigenvalue statistics of Hankel matrices for even degree monomial test functions, where the limits were Gaussian random variables.
