文章基本信息

标题：Delocalization and limiting spectral distribution of Erdős-Rényi graphs with constant expected degree
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作者：Paul Jung ; Jaehun Lee
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2018
卷号：23
DOI：10.1214/18-ECP198
语种：English
出版社：Electronic Communications in Probability
摘要：For fixed $\lambda >0$, it is known that Erdős-Rényi graphs $\{G(n,\lambda /n),n\in \mathbb{N} \}$, with edge-weights $1/\sqrt{\lambda } $, have a limiting spectral distribution, $\nu _{\lambda }$. As $\lambda \to \infty $, $\{\nu _{\lambda }\}$ converges to the semicircle distribution. For large $\lambda $, we find an orthonormal eigenvector basis of $G(n,\lambda /n)$ where most of the eigenvectors have small infinity norms as $n\to \infty $, providing a variant of an eigenvector delocalization result of Tran, Vu, and Wang (2013).