Spectral properties for the Laplacian of a generalized Wigner matrix
Spectral properties for the Laplacian of a generalized Wigner matrix
复制标题
DOI：
10.1142/s2010326322500265
复制
发表时间：
2022-07-01
影响因子：
0.9
通讯作者：
Hazra, Rajat Subhra
中科院分区：
文献类型：
--
作者：
Chatterjee, Anirban;Hazra, Rajat Subhra
在本文中，我们考虑的谱的拉普拉斯矩阵，也被称为马尔可夫矩阵的元素是独立的，但有一个方差轮廓。出于最近的工作广义维格纳矩阵，我们假设的方差轮廓产生一个序列的graphons。在这些图子收敛的假设下，我们证明了极限谱分布收敛。我们用图同态给出了极限测度的矩的表达式。在某些特殊情况下，我们明确地确定了极限。我们还研究了谱范数，并导出了最大特征值的阶。我们的结果涵盖了各种随机图的拉普拉斯算子，包括非齐次Erdos-Renyi随机图，稀疏W-随机图，随机块矩阵和约束随机图。
In this paper, we consider the spectrum of a Laplacian matrix, also known as Markov matrices where the entries of the matrix are independent but have a variance profile. Motivated by recent works on generalized Wigner matrices we assume that the variance profile gives rise to a sequence of graphons. Under the assumption that these graphons converge, we show that the limiting spectral distribution converges. 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 Laplacians of various random graphs including inhomogeneous Erdos-Renyi random graphs, sparse W-random graphs, stochastic block matrices and constrained random graphs.