Free Probability for Pairs of Faces I

By D. Voiculescu. 2013

93 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dfd84262378167af3f42a4176177dd28bced80e1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Roland Speicher
2. Ian Charlesworth
3. Brent Nelson
4. P. Skoufranis
5. Moritz Weber
6. Sven Raum

In Statistics and Probability

1. Roland Speicher
2. Ian Charlesworth
3. Brent Nelson
4. P. Skoufranis
5. Moritz Weber
6. Sven Raum

Citations in the corpus

• On Two-faced Families of Non-commutative Random Variables (2014, methodology): “To do so, we analyze the action of operators on free product spaces as in [5] to obtain explicit descriptions of Voiculescu’s universal polynomials.”
• Free Probability and Random Matrices (2014, background): “So we are, for example, not addressing such exciting topics as free stochastic and Malliavin calculus [40, 108, 114], or the rectangular version of free probability [28], or the strong version of asymptotic freeness [48, 58, 89], or free monotone transport [83], or the relation with representation t”