Invariant random subgroups of $C^{\ast }$-simple groups

Abstract

Let $\Gamma$ be a countable discrete $C^{\ast }$-simple group. Let $\mu$ be a $\Gamma$-invariant Borel probability measure on $\text{Sub}(\Gamma )$, i.e., an IRS. We show that $\mu$-almost every subgroup $H$ is $C^{\ast }$-simple.

9 pages; comments are welcome