Sparse regular random graphs: Spectral density and eigenvectors
Probability
2012-10-15 v5 Combinatorics
Abstract
We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of vertices, the empirical spectral distribution converges to the semicircle law. Moreover, we prove concentration estimates on the number of eigenvalues over progressively smaller intervals. We also show that, with high probability, all the eigenvectors are delocalized.
Cite
@article{arxiv.0910.5306,
title = {Sparse regular random graphs: Spectral density and eigenvectors},
author = {Ioana Dumitriu and Soumik Pal},
journal= {arXiv preprint arXiv:0910.5306},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AOP673 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)