The mixing time of the giant component of a random graph
Probability
2016-08-02 v2 Combinatorics
Abstract
We show that the total variation mixing time of the simple random walk on the giant component of supercritical Erdos-Renyi graphs is log^2 n. This statement was only recently proved, independently, by Fountoulakis and Reed. Our proof follows from a structure result for these graphs which is interesting in its own right. We show that these graphs are "decorated expanders" - an expander glued to graphs whose size has constant expectation and exponential tail, and such that each vertex in the expander is glued to no more than a constant number of decorations.
Keywords
Cite
@article{arxiv.math/0610459,
title = {The mixing time of the giant component of a random graph},
author = {Itai Benjamini and Gady Kozma and Nicholas Wormald},
journal= {arXiv preprint arXiv:math/0610459},
year = {2016}
}
Comments
21 pages. New version fixes a small mistake in the proof of Theorem 2.3 discovered by Johannes Blank