Sharp phase transition theorems for hyperbolicity of random groups
Abstract
Description
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.
91 pages ; 3rd version: improved redaction, corrected typos
91 pages ; 3rd version: improved redaction, corrected typos