Realizing invariant random subgroups as stabilizer distributions

. Suppose that ν is an ergodic IRS of a countable group G such that [ N G ( H ) : H ] = n < ∞ for ν -a.e. H ∈ Sub G . In this paper, we consider the question of whether ν can be realized as the stabilizer distribution of an ergodic action G ↷ ( X,µ ) on a standard Borel probability space such that the stabilizer map x (cid:55)→ G x is n -to-one.