Limit theorems for the hierarchy of freeness
Quantum Algebra
2014-07-25 v1 Mathematical Physics
math.MP
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 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.
Keywords
Cite
@article{arxiv.math/0103032,
title = {Limit theorems for the hierarchy of freeness},
author = {Uwe Franz and Romuald Lenczewski},
journal= {arXiv preprint arXiv:math/0103032},
year = {2014}
}
Comments
19 pages, latex, no figures