(1) Laboratoire de Mathématique, Université Paris-Sud, Bat. 425, 91405 Orsay Cedex, France
Abstract:
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.