Sparse random graphs: Eigenvalues and Eigenvectors

Details Sparse random graphs: Eigenvalues and Eigenvectors Sparse random graphs: Eigenvalues and Eigenvectors

2010-11-30

arxiv.org/abs/1011.6646v1

Mathematics

Combinatorics

30 pages, 3 figures

Scientific paper

In this paper we prove the semi-circular law for the eigenvalues of regular
random graph $G_{n,d}$ in the case $d\rightarrow \infty$, complementing a
previous result of McKay for fixed $d$. We also obtain a upper bound on the
infinity norm of eigenvectors of Erd\H{o}s-R\'enyi random graph $G(n,p)$,
answering a question raised by Dekel-Lee-Linial.

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