Free Probability for Pairs of Faces I

We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants, the bi-free central limit, and bi-freeness with amalgamation over an algebra B .

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 332; no. 3; pp. 955 - 980
Main Author Voiculescu, Dan-Virgil
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2014
Subjects
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Probability Space
Free Product
Regular Representation
Free Probability
Hilbert Space
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Summary:We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants, the bi-free central limit, and bi-freeness with amalgamation over an algebra B .
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-014-2060-7