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Two-parameter non-commutative Central Limit Theorem

Natasha Blitvić — 2014

Annales de l'I.H.P. Probabilités et statistiques

In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the classical Gaussian in the various non-commutative probability theories (viz. fermionic probability, Voiculescu’s free probability, and q -deformed probability of Bożejko and Speicher) all arise as the limits in a generalized Central Limit Theorem. The latter concerns sequences of non-commutative random variables (elements of a * -algebra equipped with a state) drawn from an ensemble of pair-wise commuting...

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