Vol. 283, No. 2, 2016

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A combinatorial approach to Voiculescu's bi-free partial transforms

Paul Skoufranis

Vol. 283 (2016), No. 2, 419–447
Abstract

We present a combinatorial approach to the 2-variable bi-free partial S- and T-transforms recently discovered by Voiculescu. This approach produces an alternate definition of said transforms using (,r)-cumulants.

Keywords
bi-free probability, partial bi-free $S$-transform, partial bi-free $T$-transform, bi-free convolutions
Mathematical Subject Classification 2010
Primary: 46L53, 46L54
Milestones
Received: 12 June 2015
Accepted: 8 February 2016
Published: 22 June 2016
Authors
Paul Skoufranis
Department of Mathematics
Texas A&M University
College Station, TX 77843
United States