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Generalized $$q$$-deformed Gaussian random variables. (English) Zbl 1109.46053
Bożejko, Marek (ed.) et al., Quantum probability. Papers presented at the 25th QP conference on quantum probability and related topics, Będlewo, Poland, June 20–26, 2004. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 73, 127-140 (2006).
Summary: We produce generalized $$q$$-Gaussian random variables which have two parameters of deformation. One of them is, of course, $$q$$ as for the usual $$q$$-deformation. We also investigate the corresponding Wick formulas, which will be described by some joint statistics on pair partitions.
For the entire collection see [Zbl 1101.81002].

##### MSC:
 46L53 Noncommutative probability and statistics 81S05 Commutation relations and statistics as related to quantum mechanics (general)
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