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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 19, Fasc. 1,
pages 23 - 41
 

LIMIT THEOREMS FOR THE HIERARCHY OF FREENESS

Uwe Franz
Romuald Lenczewski

Abstract: The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given m   (-  N the limit laws can be expressed in terms of non-crossing partitions of depth smaller than or equal to m. For A = C[x], we solve the associated moment problems and find explicitly the discrete limit measures.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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