Random Coxeter Groups

TL;DR

This paper extends the study of random Coxeter groups beyond right-angled cases, analyzing their homology, hyperbolicity, and FC-type properties within a probabilistic framework.

Contribution

It introduces a model for random general Coxeter groups and provides new results on their homological and geometric properties.

Findings

Analysis of homology of the nerve of random Coxeter groups

Conditions for $\, ext{delta}$-hyperbolicity in random Coxeter groups

Criteria for random Coxeter groups to have FC-type property

Abstract

Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erd\"os-R\'enyi model). In this paper, we extend this model to study random general Coxeter groups and give some results about random Coxeter groups, including some information about the homology of the nerve of a random Coxeter group and results about when random Coxeter groups are $\delta$-hyperbolic and when they have the FC-type property.