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

Volume 120 / 2010

Mihai Popa Colloquium Mathematicum 120 (2010), 319-329 MSC: 46L54, 46L53. DOI: 10.4064/cm120-2-11

Abstract

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.

Authors

  • Mihai PopaCenter 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
    e-mail

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