奇数大小$β=1$随机矩阵关联函数的一种计算方法
A method to calculate correlation functions for $β=1$ random matrices of odd size
摘要：
可以使用Pfweans来执行的用于$β=1$随机矩阵集合的关联函数的计算具有需要根据矩阵大小N的奇偶性进行单独计算的特殊特征。在计算真实高斯矩阵的Ginibre正交包络的相关性时也存在同样的复杂性。事实上，用于计算$β=1$，N奇数，相关性的方法在N奇数的情况下打破了真正的吉尼布尔矩阵，需要一个新的方法来解决这两个问题。在这项工作中采取的新方法是推导出的$β=1$，N奇数相关的限制情况下，他们的N偶对应物，当一个粒子被移向无穷大。这种方法被证明是N个奇数实高斯矩阵的相关性。
英文摘要：
The calculation of correlation functions for $β=1$ random matrix ensembles, which can be carried out using Pfaffians, has the peculiar feature of requiring a separate calculation depending on the parity of the matrix size N. This same complication is present in the calculation of the correlations for the Ginibre Orthogonal Ensemble of real Gaussian matrices. In fact the methods used to compute the $β=1$, N odd, correlations break down in the case of N odd real Ginibre matrices, necessitating a new approach to both problems. The new approach taken in this work is to deduce the $β=1$, N odd correlations as limiting cases of their N even counterparts, when one of the particles is removed towards infinity. This method is shown to yield the correlations for N odd real Gaussian matrices.
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