Algebraic & Geometric Topology 12 (2012) 979–995

DOI: 10.2140/agt.2012.12.979

Abstract

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 Erdös and Rényi model of a random graph and find precise threshold functions for hyperbolicity (or relative hyperbolicity). We also study automorphism groups of right-angled Artin groups associated to random graphs. We show that with probability tending to one as n →∞, random right-angled Artin groups have finite outer automorphism groups, assuming that the probability parameter p is constant and satisfies 0.2929 < p < 1.

Keywords

random group, right angled Artin group, hyperbolic group, automorphisms of Artin groups

Mathematical Subject Classification

Primary: 20P05

Secondary: 20F36, 57M07

References

Publication

Received: 01 February 2011
Accepted: 3 December 2011
Published: 4 May 2012

Authors