Random triangular groups at density 1/3
Group Theory
2019-02-20 v2 Combinatorics
Probability
Abstract
Let \Gamma(n,p) denote the binomial model of a random triangular group. We show that there exist constants c, C > 0 such that if p <= c/n^2, then a.a.s. \Gamma(n,p) is free and if p >= C log n/n^2 then a.a.s. \Gamma(n,p) has Kazhdan's property (T). Furthermore, we show that there exist constants C',c' > 0 such that if C'/n^2 <= p <= c' log n/n^2, then a.a.s. \Gamma(n,p) is neither free nor has Kazhdan's property (T).
Keywords
Cite
@article{arxiv.1308.5867,
title = {Random triangular groups at density 1/3},
author = {Sylwia Antoniuk and Tomasz Łuczak and Jacek Świcatkowski},
journal= {arXiv preprint arXiv:1308.5867},
year = {2019}
}