论文标题
椭圆吉尼伯集合的特征值及其重叠的过程
Eigenvalue processes of Elliptic Ginibre Ensemble and their Overlaps
论文作者
论文摘要
我们考虑了椭圆形吉尼布集合的非热基质值的过程。该模型包括戴森（Dyson）的布朗运动模型和使用墓地参数的Ginibre集合的时间演化模型。我们显示的复杂特征值过程满足随机微分方程，这些方程与戴森的模型非常相似，并提供了重叠相关性的明确形式。作为推论，在2 by-2矩阵的情况下，我们还提到了对角线重叠之间的关系，即特征值的速度和两个特征值的距离。
We consider the non-hermitian matrix-valued process of Elliptic Ginibre ensemble. This model includes Dyson's Brownian motion model and the time evolution model of Ginibre ensemble by using hermiticity parameter. We show the complex eigenvalue processes satisfy the stochastic differential equations which are very similar to Dyson's model and give an explicit form of overlap correlations. As a corollary, in the case of 2-by-2 matrix, we also mention the relation between the diagonal overlap, which is the speed of eigenvalues, and the distance of the two eigenvalues.
