Noncommutative analogues of the Law of Small Numbers for random variables indexed by elements of positive symmetric cones

Abstract

We present an analogue of the classical Law of Small Numbers, formulated for the notion of bm-independence, where the random variables are indexed by elements of positive symmetric cones in Euclidean spaces, including R d + , the Lorentz cone in Minkowski spacetime and positive definite real symmetric matrices. The geometry of the cones plays a significant role in the study as well as the combinatorics of bm-ordered partitions.