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2018 Delocalization and limiting spectral distribution of Erdős-Rényi graphs with constant expected degree
Paul Jung, Jaehun Lee
Electron. Commun. Probab. 23: 1-13 (2018). DOI: 10.1214/18-ECP198

Abstract

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).

Citation

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Paul Jung. Jaehun Lee. "Delocalization and limiting spectral distribution of Erdős-Rényi graphs with constant expected degree." Electron. Commun. Probab. 23 1 - 13, 2018. https://doi.org/10.1214/18-ECP198

Information

Received: 21 August 2018; Accepted: 19 November 2018; Published: 2018
First available in Project Euclid: 15 December 2018

zbMATH: 1405.05162
MathSciNet: MR3896830
Digital Object Identifier: 10.1214/18-ECP198

Subjects:
Primary: 05C80, 15B52, 60B20

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