论文标题
弱非热性的复杂椭圆吉尼伯集合：散装间距分布
The complex elliptic Ginibre ensemble at weak non-Hermiticity: bulk spacing distributions
论文作者
论文摘要
我们表明，从复杂的椭圆形吉尼布集合中绘制的随机矩阵的对成对之间的散装间距的分布是渐近地通过弱弱的非词性的限制的Gaudin-Mehta分布的概括来给出的。 The same generalization is expressed in terms of an integro-differential Painlevé function and it is shown that the generalized Gaudin-Mehta distribution describes the crossover, with increasing degree of non-Hermiticity, from Gaudin-Mehta nearest-neighbor bulk statistics in the Gaussian Unitary Ensemble to Poisson gap statistics for eigenvalue real parts in the bulk of the Complex Ginibre Ensemble.
We show that the distribution of bulk spacings between pairs of adjacent eigenvalue real parts of a random matrix drawn from the complex elliptic Ginibre ensemble is asymptotically given by a generalization of the Gaudin-Mehta distribution, in the limit of weak non-Hermiticity. The same generalization is expressed in terms of an integro-differential Painlevé function and it is shown that the generalized Gaudin-Mehta distribution describes the crossover, with increasing degree of non-Hermiticity, from Gaudin-Mehta nearest-neighbor bulk statistics in the Gaussian Unitary Ensemble to Poisson gap statistics for eigenvalue real parts in the bulk of the Complex Ginibre Ensemble.
