随机图中正则Laplace矩阵的谱分析

Spectral Analysis of Normalized Laplacian Matrix in Random Graphs

用随机矩阵中的矩方法研究给定期望度数随机图中正则Laplace矩阵经验谱分布的收敛性,结果表明,在期望度数满足一定条件时,相应正则Laplace矩阵的经验谱分布几乎处处收敛到固定的概率分布,但在不同的期望度数下,此概率分布可能不同.

We investigated the convergence of the empirical spectral distribution （ESD）of normalized Laplacian matrix from random graph with given expected degree.It was shown that the ESD of normalized Laplacian matrix converges to a fixed probability distribution when the expected degree satisfys some assumptions,but the fixed probability distribution may be different at different places.