Sharp phase transition theorems for hyperbolicity of random groups
Ollivier, Yann
HAL, hal-00138227 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR],  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00138227,
     author = {Ollivier, Yann},
     title = {Sharp phase transition theorems for hyperbolicity of random groups},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00138227}
}

Ollivier, Yann. Sharp phase transition theorems for hyperbolicity of random groups. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00138227/