论文标题
Ginibre合奏I：Ginue的研究进展
Progress on the study of the Ginibre ensembles I: GinUE
论文作者
论文摘要
Ginibre单一合奏（Ginue）由$ n \ times n $随机矩阵组成，具有独立的复杂标准高斯条目。这是由Ginbre在1965年引入的，Ginbre表明特征值形成具有显式相关核的确定点过程，并且在缩放量表后，它们在恒定密度的单位磁盘上受支持。一段时间以来，人们对Ginue在随机矩阵理论中的应用和其理论的丰富性都具有基本地位。在这里，我们回顾了与Ginue研究有关的许多主题的进展。这些是特征值概率密度函数和相关函数，波动公式，相关函数的总规则和渐近行为以及正常矩阵模型。我们在量子中也讨论了许多身体物理和量子混乱的应用，并说明了特征向量的某些统计特性。
The Ginibre unitary ensemble (GinUE) consists of $N \times N$ random matrices with independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre, who showed that the eigenvalues form a determinantal point process with an explicit correlation kernel, and after scaling they are supported on the unit disk with constant density. For some time now it has been appreciated that GinUE has a fundamental place within random matrix theory, both for its applications and for the richness of its theory. Here we review the progress on a number of themes relating to the study of GinUE. These are eigenvalue probability density functions and correlation functions, fluctuation formulas, sum rules and asymptotic behaviours of correlation functions, and normal matrix models. We discuss too applications in quantum many body physics and quantum chaos, and give an account of some statistical properties of the eigenvectors.
