Geodesic
Freeness with amalgamation, limit theorems and $S$-transform in non-commutative probability spaces of type B
Mihai Popa1
1 Center for Advanced Studies in Mathematics Ben Gurion University of the Negev P.O.B. 653 Be'er Sheva 84105, Israel and Institute of Mathematics “Simion Stoilow” of the Romanian Academy P.O. Box 1-764 RO-014700 Bucureşti, Romania
Colloquium Mathematicum, Tome 120 (2010) no. 2, pp. 319-329.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The paper addresses several problems left open by P. Biane, F. Goodman and A. Nica [Trans. Amer. Math. Soc. 355 (2003)]. 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 analogues to the Central Limit Theorem and Poisson Limit Theorem.
DOI : 10.4064/cm120-2-11
Keywords: paper addresses several problems biane goodman nica trans amer math soc main result type non commutative probability space studied framework freeness amalgamation view allows easy ways constructing version s transform proving analogues central limit theorem poisson limit theorem

Mihai Popa 1

1 Center for Advanced Studies in Mathematics Ben Gurion University of the Negev P.O.B. 653 Be'er Sheva 84105, Israel and Institute of Mathematics “Simion Stoilow” of the Romanian Academy P.O. Box 1-764 RO-014700 Bucureşti, Romania 
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Mihai Popa. Freeness with amalgamation, limit theorems
 and $S$-transform
 in non-commutative probability spaces of type B. Colloquium Mathematicum, Tome 120 (2010) no. 2, pp. 319-329. doi : 10.4064/cm120-2-11. http://geodesic.mathdoc.fr/articles/10.4064/cm120-2-11/

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