Coxeter Groups and Random Groups
Danny Calegari · Princeton University Press eBooks · 2020
For every dimension d, there is an infinite family of convex cocompact reflection groups of isometries of hyperbolic d-space -the superideal (simplicial and cubical) reflection groups -with the property that a random group at any density less than a half (or in the few relators model) contains quasiconvex subgroups commensurable with some member of the family, with overwhelming probability.