Sharp phase transition theorems for hyperbolicity of random groups

Details Sharp phase transition theorems for hyperbolicity of random groups Sharp phase transition theorems for hyperbolicity of random groups

2003-01-17

arxiv.org/abs/math/0301187v3

Mathematics

Group Theory

91 pages ; 3rd version: improved redaction, corrected typos

Scientific paper

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.

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