Freeness with amalgamation, limit theorems and S-transform in non-commutative probability spaces of type B

Details Freeness with amalgamation, limit theorems and S-transform in non-commutative probability spaces of type B Freeness with amalgamation, limit theorems and S-transform in non-commutative probability spaces of type B

2007-08-31

arxiv.org/abs/0709.0011v2

Mathematics

Operator Algebras

Scientific paper

The present material addresses several problems left open in the Trans. AMS paper " Non-crossing cumulants of type B" of P. Biane, F. Goodman and A. Nica. The main result is that a type B non-commutative probability space can be studied in the framework of freeness with amalgamation. This view allows easy ways of constructing a version of the S-transform as well as proving analogue results to Central Limit Theorem and Poisson Limit Theorem.

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