Appears in collection : Group Actions and Rigidity: Around the Zimmer Program / Actions de Groupes et Rigidité : Autour du programme de Zimmer

I will explain how certain probabilistic methods can be used to study the discrete groups of semisimple Lie groups. I will define the space of subgroups with the Chabauty topology and introduce two useful classes of random subgroups - invariant ans stationary random subgroups. In higher rank thses classes admit nice classification witch can be usesd to prove that a confined subgroup of a simple higher rank group must be a lattice.