论文标题
tracy-widom定律，用于大型信号加词矩阵的极端特征值
Tracy-Widom law for the extreme eigenvalues of large signal-plus-noise matrices
论文作者
论文摘要
令$ \ by = \ br+\ bx $为$ m \ times n $矩阵，其中$ \ br $是矩形对角线矩阵，$ \ bx $由$ i.i.d. $ entries组成。这是一个信号加上噪声类型的模型。它的信号矩阵可能是完整的等级，与低级案例相比，文献中很少研究。本文是为了研究$ \ by \ by^*$的极端特征值。我们表明，在高维设置（$ m/n \ rightarrow c \ in（0,1] $）和一些规律性条件下，$ \ br $的某些规律性条件将重新缩放的极端特征值在分发中分配到Tracy-Widom分发（$ TW_1 $）。
Let $\bY =\bR+\bX$ be an $M\times N$ matrix, where $\bR$ is a rectangular diagonal matrix and $\bX$ consists of $i.i.d.$ entries. This is a signal-plus-noise type model. Its signal matrix could be full rank, which is rarely studied in literature compared with the low rank cases. This paper is to study the extreme eigenvalues of $\bY\bY^*$. We show that under the high dimensional setting ($M/N\rightarrow c\in(0,1]$) and some regularity conditions on $\bR$ the rescaled extreme eigenvalue converges in distribution to Tracy-Widom distribution ($TW_1$).
