论文标题
大型随机基质的光谱半径的精确渐近物
Precise asymptotics for the spectral radius of a large random matrix
论文作者
论文摘要
我们考虑具有独立的，相同分布的条目的大型随机矩阵$ x $的光谱半径。我们表明，它的典型大小由精确的三届渐近学给出，其最佳误差术语超出了著名的循环定律的半径。这种渐近学的系数是通用的，但它们与最近的类似渐近学有所不同，因为[29]中最右边的$ x $的特征值证明。为了访问更复杂的光谱半径，我们需要使用Dyson Brownian Motion为不同的复杂移位参数$ Z $建立一个新的去相关机制，用于$ X-Z $的低ly式奇异值。
We consider the spectral radius of a large random matrix $X$ with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of $X$ in [29]. To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of $X-z$ for different complex shift parameters $z$ using the Dyson Brownian Motion.
