Random groups and Property (T): \.Zuk's theorem revisited
Group Theory
2013-08-06 v2
Abstract
We provide a full and rigorous proof of a theorem attributed to \.Zuk, stating that random groups in the Gromov density model for d > 1/3 have property (T) with high probability. The original paper had numerous gaps, in particular, crucial steps involving passing between different models of random groups were not described. We fix the gaps using combinatorial arguments and a recent result concerning perfect matchings in random hypergraphs. We also provide an alternative proof, avoiding combinatorial difficulties and relying solely on spectral properties of random graphs in G(n, p) model.
Keywords
Cite
@article{arxiv.1106.2242,
title = {Random groups and Property (T): \.Zuk's theorem revisited},
author = {Marcin Kotowski and Michal Kotowski},
journal= {arXiv preprint arXiv:1106.2242},
year = {2013}
}
Comments
v2: minor corrections