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Free Probability for Pairs of Faces I

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, University of California at Berkeley, Berkeley, CA, 94720-3840, USA

    Dan-Virgil Voiculescu

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  1. Dan-Virgil Voiculescu
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Correspondence to Dan-Virgil Voiculescu.

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Communicated by Y. Kawahigashi

Research supported in part by NSF Grant DMS-1301727.

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Voiculescu, DV. Free Probability for Pairs of Faces I. Commun. Math. Phys. 332, 955–980 (2014). https://doi.org/10.1007/s00220-014-2060-7

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  • DOI: https://doi.org/10.1007/s00220-014-2060-7

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