Sharp phase transition theorems for hyperbolicity of random groups
群论
2007-05-23 v3 概率论
摘要
We prove that in various natural models of a random quotient of a group, depending on a density parameter, for each hyperbolic group there is some critical density under which a random quotient is still hyperbolic with high probability, whereas above this critical value a random quotient is very probably trivial. We give explicit characterizations of these critical densities for the various models.
引用
@article{arxiv.math/0301187,
title = {Sharp phase transition theorems for hyperbolicity of random groups},
author = {Yann Ollivier},
journal= {arXiv preprint arXiv:math/0301187},
year = {2007}
}
备注
91 pages ; 3rd version: improved redaction, corrected typos