Random groups arising as graph products

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 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 $0.2929<p<1$.

References in corpus (2)

• Peak reduction and finite presentations for automorphism groups of right-angled Artin groups
• Random quotients of the modular group are rigid and essentially incompressible

Cited by in corpus (11)

• Thickness, relative hyperbolicity, and randomness in Coxeter groups
• Quasi-isometric classification of right-angled Artin groups I: the finite out case
• Global Structural Properties of Random Graphs
• Relative automorphism groups of right-angled Artin groups
• Groups quasi-isometric to RAAG's
• Random graph products of finite groups are rational duality groups
• Finiteness of outer automorphism groups of random right-angled Artin groups
• Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups
• Trees, homology, and automorphism groups of RAAGs
• A note on virtual duality and automorphism groups of right-angled Artin groups
• Random Artin groups