We present a generalization of the classical central limit theorem to the case of non-commuting random variables which are bm-independent and indexed by a partially ordered set. As the set of indices I we consider discrete lattices in symmetric positive cones, with the order given by the cones. We show that the limit measures have moments which satisfy recurrences generalizing the recurrence for the Catalan numbers.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-24,
author = {Janusz Wysocza\'nski},
title = {bm-independence and central limit theorems associated with symmetric cones},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {315-320},
zbl = {1140.46328},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-24}
}
Janusz Wysoczański. bm-independence and central limit theorems associated with symmetric cones. Banach Center Publications, Tome 75 (2007) pp. 315-320. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-24/