Invariant random subgroups in Coxeter groups

Geometric limits of Coxeter polyhedra in hyperbolic space are (possibly infinite-volume) polyhedra. This can be make precise in the setting of Benjamini—Schramm convergence of subgroups. The limit objects are then described more precisely as "invariant random subgroups" supported on Coxeter subgroups. They seem to be easier to study than general invariant random subgroups of hyperbolic lattices, and they allow to construct examples of such with some notable features. In this talk I will attempt to put these objects in context and describe several such examples.