bm-CENTRAL LIMIT THEOREMS ASSOCIATED WITH
NON-SYMMETRIC POSITIVE CONES
Lahcen Oussi
Janusz Wysoczański
Abstract: Analogues of the classical Central Limit Theorem are proved in the noncommutative
setting of random variables which are bm-independent 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.
2000 AMS Mathematics Subject Classification: Primary: 60F05; Secondary: 60C05,
05B30, 06A06, 06A07.
Keywords and phrases: Noncommutative probability, central limit theorem,
bm-independence, non-symmetric positive cones, Vinberg cone, circular cone.