Invariant random subgroups of the free group

Abstract

Let $G$ be a locally compact group. A random closed subgroup with conjugation-invariant law is called an invariant random subgroup or IRS for short. We show that each nonabelian free group has a large “zoo” of IRS’s. This contrasts with results of Stuck and Zimmer which show that there are no non-obvious IRS’s of higher rank semisimple Lie groups with property (T).