We state and prove a noncommutative limit theorem for correlations which are homogeneous with respect to order-preserving injections. The most interesting examples of central limit theorems in quantum probability (for commuting, anticommuting, and free independence and also various q-qclt's), as well as the limit theorems for the Poisson law and the free Poisson law are special cases of the theorem. In particular, the theorem contains the q-central limit theorem for non-identically distributed variables, derived in our previous work in the context of q-bialgebras and quantum groups. More importantly, new examples of limit theorems of q-Poisson type are derived for both the infinite tensor product algebra and the reduced free product, leading to new q-laws. In the first case the limit as q → 1 is studied in more detail and a connection with partial Bell polynomials is established.
@article{bwmeta1.element.bwnjournal-article-smv129i3p225bwm,
author = {Romuald Lenczewski},
title = {A noncommutative limit theorem for homogeneous correlations},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {225-252},
zbl = {0912.60046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv129i3p225bwm}
}
Lenczewski, Romuald. A noncommutative limit theorem for homogeneous correlations. Studia Mathematica, Tome 129 (1998) pp. 225-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv129i3p225bwm/
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