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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 39, Fasc. 12,
pages 183 - 197
DOI: 10.19195/0208-4147.39.1.12
 

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.

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