广义Wigner矩阵的经验谱分布的收敛速度

发布时间：2018-04-20 00:30

本文选题：经验谱分布函数 + 极限谱分布函数　；参考：《东北师范大学》2017年硕士论文

【摘要】：Wn是一个n × n埃尔米特随机矩阵,Wn矩阵中包含对角线的上三角元素均为独立复数随机变量,并且其均值为0、方差为1. Tn是一个n × n的非随机的正定埃尔米特矩阵.假设,当n → ∞时,Tn的特征值的经验分布收敛于一个概率分布.定义An=n-1/2Tn1/2WnTn1/2.然后借助Stieltjes变换,我们可以得到,如果当n → ∞时,如果supnsupi,jE|xij16| ∞,我们得到,An的经验谱分布的期望收敛于它的极限谱分布的速度为O(n-1/5).
[Abstract]:Wn is a n x n Hermite random matrix. The upper trigonometric elements containing diagonal lines are both independent complex random variables, and their mean value is 0 and the variance is 1. Tn is a non random positive definite matrix of n * n. Suppose, when n to infinity, the empirical distribution of the eigenvalues of Tn is convergent to a probability distribution. An=n-1/ is defined as An=n-1/. 2Tn1/2WnTn1/2. then with the help of Stieltjes transformation, we can get that if, when n - infinity, if supnsupi, jE|xij16| infinity, we get, the expectation of the empirical spectrum distribution of An converges to the velocity of its limit spectrum distribution is O (n-1/5).

【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C81

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