Soft Barycentric Universality
The Barycentric Central Limit theorem works also for soft Barycentric refinements. This refinement had been motivated to find triangulated dual manifolds: take all the simplices except the ones of one less than the maximal dimension and connect two if one is contained in the other or if their intersection has dimension one less than the maximal dimension. It has the interesting feature that the vertex degrees of a 2 manifold remains bounded so that we have a continuous limiting density of states. As for now, I know that it exists and that experiments show that the density of states is piecewise linear on the interval [0,9]. As a reminder, For Barycentric refinements in one dimensions, we had the arcsin distribution on [0,4] which is the equilibrium meaure on that interval.
The footage at the beginning and end were taken during a detour over Tufts while biking home to Arlington.