Limit theorems for the hierarchy of freeness

Details Limit theorems for the hierarchy of freeness Limit theorems for the hierarchy of freeness

2001-03-06

arxiv.org/abs/math/0103032v1

Prob. Math. Stat. Vol.19 (1999), 23-41

Mathematics

Quantum Algebra

19 pages, latex, no figures

Scientific paper

The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given natural m the limit laws can be expressed in terms of non-crossing partitions of depth smaller or equal to m. For the algebra of polynomials in one variable we solve the associated moment problems and find explicitly the discrete limit measures.

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