On Q-independence, limit theorems and q-Gaussian distribution
Studia Mathematica (1998)
- Volume: 129, Issue: 2, page 113-135
- ISSN: 0039-3223
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topMarciniak, Marcin. "On Q-independence, limit theorems and q-Gaussian distribution." Studia Mathematica 129.2 (1998): 113-135. <http://eudml.org/doc/216494>.
@article{Marciniak1998,
abstract = {We formulate the notion of Q-independence which generalizes the classical independence of random variables and free independence introduced by Voiculescu. Here Q stands for a family of polynomials indexed by tiny partitions of finite sets. The analogs of the central limit theorem and Poisson limit theorem are proved. Moreover, it is shown that in some special cases this kind of independence leads to the q-probability theory of Bożejko and Speicher.},
author = {Marciniak, Marcin},
journal = {Studia Mathematica},
keywords = {-independence; probability system; independence of random variables; central limit theorem; Poisson limit theorem},
language = {eng},
number = {2},
pages = {113-135},
title = {On Q-independence, limit theorems and q-Gaussian distribution},
url = {http://eudml.org/doc/216494},
volume = {129},
year = {1998},
}
TY - JOUR
AU - Marciniak, Marcin
TI - On Q-independence, limit theorems and q-Gaussian distribution
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 2
SP - 113
EP - 135
AB - We formulate the notion of Q-independence which generalizes the classical independence of random variables and free independence introduced by Voiculescu. Here Q stands for a family of polynomials indexed by tiny partitions of finite sets. The analogs of the central limit theorem and Poisson limit theorem are proved. Moreover, it is shown that in some special cases this kind of independence leads to the q-probability theory of Bożejko and Speicher.
LA - eng
KW - -independence; probability system; independence of random variables; central limit theorem; Poisson limit theorem
UR - http://eudml.org/doc/216494
ER -
References
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- [17] D. Voiculescu, Symmetries of some reduced free products of C*-algebras, in: H. Araki et al. (eds.), Operator Algebras and their Connection with Topology and Ergodic Theory (Romania, 1983), Lecture Notes in Math. 1132, Springer, Berlin, 1985, 556-588.
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