Apparaît dans la collection : 2014 - T1 - WS1 - Asymptotic properties of groups

After a short introduction to invariant random subgroups (IRS) I will present some results obtained in collaboration with L. Bowen, R. Kravchenko and T. Nagnibeda and with M. Benli and T. Nagnibeda. First I will talk about IRS of groups of lamplighter type. Then about IRSof groups of intermediate growth. And finally, about IRS on hyperbolic groups, mapping class group and group of outer automorphisms of a free group. The latter results are based on study of characteristic random subgroups of a free abelian group of infinite rank and of a free non-commutative group.