标题： 实非对称矩阵的稀疏高斯系综的谱分布 显示英文标题

标题： Spectral distribution of sparse Gaussian Ensembles of Real Asymmetric Matrices

摘要： 生物和人工神经网络的理论分析，例如 对突触或权重矩阵的建模需要考虑通用的实非对称矩阵集合，这些集合中的矩阵元素具有不同的顺序，例如 稀疏结构或带状结构。 我们采用复杂性参数方法来分析实非对称矩阵的多参数高斯系综的谱统计特性，并推导出实数以及复数特征值的系综平均谱密度。 对具有任意均值和方差的矩阵元素的考虑使我们能够自由地在系综中建模所需的稀疏性。 我们的公式为广泛范围的稀疏实非对称系综的谱统计提供了共同的数学公式，并且 从而揭示了它们之间深层次的普遍性。 显示英文摘要

摘要： Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a sparse structure or a banded structure. We pursue the complexity parameter approach to analyze the spectral statistics of the multiparametric Gaussian ensembles of real asymmetric matrices and derive the ensemble averaged spectral densities for real as well as complex eigenvalues. Considerations of the matrix elements with arbitrary choice of mean and variances render us the freedom to model the desired sparsity in the ensemble. Our formulation provides a common mathematical formulation of the spectral statistics for a wide range of sparse real-asymmetric ensembles and also reveals, thereby, a deep rooted universality among them.