Virtually fibering random right-angled Coxeter groups

Abstract

We show that the Right-Angled Coxeter group $C=C(G)$ associated to a random graph $G\sim \mathcal{G}(n,p)$ with $\frac{\log n + \log\log n + ω(1)}{n} \leq p < 1- ω(n^{-2})$ virtually algebraically fibers. This means that $C$ has a finite index subgroup $C'$ and a finitely generated normal subgroup $N\subset C'$ such that $C'/N \cong \mathbb{Z}$. We also obtain the corresponding hitting time statements, more precisely, we show that as soon as $G$ has minimum degree at least 2 and as long as it is not the complete graph, then $C(G)$ virtually algebraically fibers. The result builds upon the work of Jankiewicz, Norin, and Wise and it is essentially best possible.