${\mathrm{\ell }}^2$ Betti numbers and coherence of random groups

We study ${\mathrm{\ell }}^2$ Betti numbers, coherence, and virtual fibring of random groups in the few-relator model. In particular, random groups with negative Euler characteristic are coherent, have ${\mathrm{\ell }}^2$ homology concentrated in dimension 1, and embed in a virtually free-by-cyclic group with high probability. Similar results are shown with positive probability in the zero Euler characteristic case.