Strongly convergent unitary representations of right-angled Artin groups

Abstract

We prove using a novel random matrix model that all right-angled Artin groups have a sequence of finite dimensional unitary representations that strongly converge to the regular representation. We deduce that this result applies also to: the fundamental group of a closed hyperbolic manifold that is either three dimensional or standard arithmetic type, any Coxeter group, and any word-hyperbolic cubulated group. There are applications of this to the spectral geometry of e.g. hyperbolic 3-manifolds.Comment: 35 pages, 1 figur