非厄米特稀疏矩阵谱密度的腔方法
Cavity approach to the spectral density of non-Hermitian sparse matrices
摘要：
利用腔方法分析了非厄米特稀疏随机矩阵系综的谱密度。我们提出了一组方程，从该方程可以有效地和准确地计算给定系综的谱密度。在这种方法中，广义的Girko定律很容易恢复。我们比较我们的结果与直接对角化的随机矩阵合奏，发现非常好的协议。
英文摘要：
The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated. Within this approach, the generalised Girko's law is recovered easily. We compare our results with direct diagonalisation for a number of random matrix ensembles, finding excellent agreement.
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