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arXiv · math/0610459

The mixing time of the giant component of a random graph

Itai Benjamini·Gady Kozma·Nicholas Wormald
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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.

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Itai Benjamini, Gady Kozma, Nicholas Wormald. 2016-07-31. The mixing time of the giant component of a random graph. https://arxiv.org/abs/math/0610459

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