Graph matrices are a type of matrix which has played a crucial role in analyzing the sum of squares hierarchy on average case problems. However, except for rough norm bounds, little is known about graph matrices. In this paper, we take a step towards better understanding graph matrices by determining the limiting distribution of the spectrum of the singular values of Z-shaped graph matrices. We then give a partial generalization of our results for $m$-layer Z-shaped graph matrices.

翻译：图矩阵是一类在分析平均情况问题中平方和层次结构方面发挥关键作用的矩阵。然而，除粗略的范数界外，目前对图矩阵知之甚少。本文通过确定Z形图矩阵奇异值谱的极限分布，朝着更好地理解图矩阵迈进一步。随后，我们对$m$层Z形图矩阵的结果给出了部分推广。