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 the limit laws can
be expressed in terms of non-crossing partitions of depth smaller than or equal to For
we solve the associated moment problems and find explicitly the discrete limit
measures.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -