Appears in collection : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens

We are interested in studying the behavior of geometric invariants of hyperbolic 3-manifolds, such as the length of their geodesics. A way to do so is by using probabilistic methods. That is, we consider a set of hyperbolic manifolds, put a probability measure on it, and ask what is the probability that a random manifold has a certain property. There are several models of random manifolds. In this talk, I will explain one of the principal probabilistic models for 3 dimensions and I will present a result concerning the length spectrum - the set of lengths of all closed geodesics - of a 3-manifold constructed under this model.