Sharp threshold for percolation on expanders
Probability
2012-09-26 v2
Abstract
We study the appearance of the giant component in random subgraphs of a given large finite graph G=(V,E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c in ]0,1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.
Cite
@article{arxiv.0906.3657,
title = {Sharp threshold for percolation on expanders},
author = {Itai Benjamini and Stéphane Boucheron and Gábor Lugosi and Raphaël Rossignol},
journal= {arXiv preprint arXiv:0906.3657},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOP610 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)