Characteristic random subgroups of geometric groups and free abelian groups of infinite rank

Abstract

We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then $G$ has $2^{{\aleph }_0}$ many continuous ergodic invariant random subgroups. If $G$ is a nonabelian free group then $G$ has $2^{{\aleph }_0}$ many continuous $G$-ergodic characteristic random subgroups. We also provide a complete classification of characteristic random subgroups of free abelian groups of countably infinite rank and elementary $p$-groups of countably infinite rank.

Comments welcome! This new version classifies automorphism-invariant random subspaces of a locally compact vector space over a finite field and computes finite marginals

Cited by in corpus (3)

• Invariant random subgroups of linear groups
• Generic IRS in free groups, after Bowen
• Invariant random subgroups of groups acting on hyperbolic spaces