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Freeness with amalgamation, limit theorems and $S$-transform in non-commutative probability spaces of type B
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
Colloquium Mathematicum, Tome 120 (2010) no. 2, pp. 319-329 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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

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