论文标题
广义Wigner基质的Laplacian的光谱特性
Spectral properties of the Laplacian of a generalized Wigner matrix
论文作者
论文摘要
在本文中，我们考虑了独立假设下的拉普拉斯基质（也称为马尔可夫矩阵）的光谱。我们假设条目具有差异。在最新的广义Wigner矩阵上的动机中，我们假设方差曲线会产生一系列图形子。在这些图形收敛的假设下，我们表明了缩放拉普拉斯的限制光谱分布。我们以图形同态的限制度量矩表达了一种表达。在某些特殊情况下，我们明确确定限制。我们还研究光谱规范并得出最大特征值的顺序。我们表明，我们的结果涵盖了各种随机图的拉普拉斯式，包括不均匀的erdős-r \'enyi随机图，稀疏的w-random图，随机块矩阵和约束随机图。
In this article we consider the spectrum of a Laplacian matrix, also known as the Markov matrix, under the independence assumption. We assume that the entries have a variance profile. Motivated by recent works on generalized Wigner matrices we assume that variance profile gives rise to a sequence of graphons. Under the assumption that these graphons converge, we show that the limiting spectral distribution of the scaled Laplacian converge. We give an expression for the moments of the limiting measure in terms of graph homomorphisms. In some special cases we identify the limit explicitly. We also study the spectral norm and derive the order of the maximum eigenvalue. We show that our results cover Laplacian of various random graphs include inhomogeneous Erdős- R\' enyi random graph, sparse W-random graphs, stochastic block matrices and constrained random graphs.
