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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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