论文标题
大型自动协方差矩阵的特征值分布
On eigenvalue distributions of large auto-covariance matrices
论文作者
论文摘要
在本文中，我们为一类自动协方差矩阵的特征值建立了限制分布。在文献中为这些自动协方差矩阵的正则版本发现了相同的分布。原始的非规范自动辅助矩阵是不可逆转的，它通过Girko的隐居方案引入了补充难度，以研究其特征值。本文的关键结果是一种新的多项式下限，该结合对于与随机矩阵的等级缺陷二次函数相关的分解矩阵的最小奇异值，具有独立且相同分布的条目。本文的另一个改进是，自动辅助矩阵的滞后可以随矩阵维度增长到无穷大。
In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original non-regularized auto-covariance matrices are non invertible which introduce supplementary diffculties for the study of their eigenvalues through Girko's Hermitization scheme. The key result in this paper is a new polynomial lower bound for the least singular value of the resolvent matrices associated to a rank-defective quadratic function of a random matrix with independent and identically distributed entries. Another improvement in the paper is that the lag of the auto-covariance matrices can grow to infinity with the matrix dimension.
