Linear representations of random groups

We show that for a fixed k ∈ N, Gromov random groups with any density d > 0 have no nontrivial degree k representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when d < ¹₆ such groups have a faithful linear representation over Q, a.a.s.