Abstract
Algebr. Geom. Topol. 12 (2012) 979-995 In this paper we study the hyperbolicity properties of a class of random
groups arising as graph products associated to random graphs. Recall, that the
construction of a graph product is a generalization of the constructions of
right-angled Artin and Coxeter groups. We adopt the Erdos - Renyi model of a
random graph and find precise threshold functions for the hyperbolicity (or
relative hyperbolicity). We aslo study automorphism groups of right-angled
Artin groups associated to random graphs. We show that with probability tending
to one as $n\to \infty$, random right-angled Artin groups have finite outer
automorphism groups, assuming that the probability parameter $p$ is constant
and satisfies $0.2929 <p<1$.