We consider large neural networks in cognitive neuropsychology whose synaptic connectivity matrices are randomly chosen from correlated Gaussian random matrices. We focus on the moments of characteristic polynomials and prove that the limiting even and odd moments at the edge are given by the largest eigenvalue distribution in the Gaussian Symplectic Ensemble (GSE) and in the induced GSE ensemble, respectively. Our results show that there exists a duality relation between the real Ginibre ensemble and the GSE ensemble via the moment of characteristic polynomials and the largest eigenvalue.

中文翻译：

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某些随机神经网络中特征多项式的矩

我们认为认知神经心理学中的大型神经网络的突触连接矩阵是从相关的高斯随机矩阵中随机选择的。我们专注于特征多项式的矩，并证明边缘的极限偶数和奇数矩分别由高斯辛集合（GSE）和感生GSE集合中的最大特征值分布给出。我们的结果表明，通过特征多项式和最大特征值的时刻，真实的Ginibre集合与GSE集合之间存在对偶关系。