| 1. | In the random matrix theory , the 1 - level correlation functions
在随机矩阵理论中， 1 -级相关函数 |
| 2. | Identify the core random matrix question that needs to be solved to tackle the generalization
识别随机矩阵核心问题，解决它们以处理一般性问题。 |
| 3. | Mention what other generalizations of the random matrix problem are interesting but not discussed
提及其它有趣的但没被提到的随机矩阵的一般化问题。 |
| 4. | This course is an introduction to the basics of random matrix theory , motivated by engineering and scientific applications
这门课是为了工程和科学应用，是一门介绍随机矩阵理论基础的课程。 |
| 5. | The topics represented are by no means exhaustive but are meant to be indicative of the work done by researchers in diverse communities involving random matrix theory
这些课题不能说是完全无遗漏的，但可以看到各领域的研究人员用随机矩阵论所做的工作。 |
| 6. | To expose the statistical properties of the degenerated spectrum , with the aid of the random matrix theory , a possible form of the nns distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same - degeneracy case
利用随机矩阵理论，通过对一特殊情形的简并谱展开研究，得到了简并谱一种可能的最小相邻间距nns分布函数。 |
| 7. | To expose the statistical properties of the degenerated spectrum , with the aid of the random matrix theory , a possible form of the nns distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same - degeneracy case
摘要利用随机矩阵理论，通过对一特殊情形的简并谱展开研究，得到了简并谱一种可能的最小相邻间距nns分布函数。 |
| 8. | It is has been known that the energy spectra statistic of a chaotic system agrees with wigner distribution which is achieved from random matrix theory and the one of a integrable system is poisson distribution achieved originally from the irregular spectra
一个经典混沌系统的量子能谱统计分布满足由随机矩阵理论所导出的winger分布，而可积系统满足无规能谱的统计分布即泊松分布。 |
| 9. | On the strength of the square loss function , this part also defines the vector loss function and matrix loss function , and discusses the bayesian risk decision solutions about random vector parameter and random matrix parameter under these loss functions respectively . secondly , the bayesian inference theory about single equation model is explored
在单参数平方损失函数的基础上，定义了向量损失函数，利用向量化算子vec定义了矩阵损失函数，并讨论了这两类损失函数下随机向量参数和随机矩阵参数的贝叶斯风险决策解。 |
| 10. | Chapter 5 is focused on the studies on the equivalent conditions for maximum value convergence of sums of independent random matrix sequences , and the sufficiency condition of the strong consistency of m estimator of regression parametric in linear model for negatively associate samples , thus enriching and strengthening the results of a series of papers
第五章得到了独立阵列和（含加权和）的最大值完全收敛的等价条件，从而丰富和强化了前人的一系列结果获得了负相关样本线性模型中回归参数m估计是强相合的较弱的充分条件 |
