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Title

On Q-independence, limit theorems and q-Gaussian distribution

Authors 1

Affiliations

  1. Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

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.

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Studia Mathematica
1998/129/2
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Pages:
113-135
Main language of publication
English
Received
1996-10-15
Accepted
1997-11-24
Published
1998
Exact and natural sciences