The length spectrum of random hyperbolic 3-manifolds

We study the length spectrum of a model of random hyperbolic 3-manifolds introduced by Petri and Raimbault. These are compact manifolds with boundary constructed by randomly gluing truncated tetrahedra along their faces. We prove that, as the volume tends to infinity, their length spectrum converge in distribution to a Poisson point process on ${\mathbb{R}}_{\ge 0}$, with computable intensity $\lambda$.