Co-spectral radii and subgroup intersections,

 

A subgroup H of a countable group G is co-amenable if the left regular representation on the coset space G/H admits almost invariant vectors. Co-amenablility is a notion of largeness of a subgroup, but it is not the best behaved one. For example, the intersections of co-amenable subgroups can fail to be co-amenable. I will talk about a joint work with Wouter van Limbeek in which we prove that the class of co-amenable invariant random subgroups is closed under taking finite intersection. This follows from more general results on the co-spectral radii of intersections of invariant random subgroups.