On invariant random positive definite functions

27 Apr 2018 · Alekseev Vadim, Brugger Rahel ·

We give the definition of an invariant random positive definite function on a discrete group, generalizing both the notion of an invariant random subgroup and a character. We use von Neumann algebras to show that all invariant random positive definite functions on groups with infinite conjugacy classes which integrate to the regular character are constant.