Analogues of the classical Central Limit Theorem are proved in the noncommutative setting of random variables which are bmindependent and indexed by elements of positive non-symmetric cones, such as the circular cone, sectors in Euclidean spaces and the Vinberg cone. The geometry of the cones is shown to play a crucial role and the related volume characteristics of the cones is shown.

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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.