Random groups in the square model have property (T) at densities over $\frac{5}{12}$

Damian Orlef, Tomasz Odrzygóźdź

A random group in the square model $\mathcal{Q}(n,d)$ is given by a presentation with $n$ generators and a uniformly random set of $(2n-1{)}^{4d}$ cyclically reduced relators of leng…