随机图中正则Laplace矩阵的谱分析

摘要

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.%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。