CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

On Two-faced Families of Non-commutative Random Variables

  Published:2015-09-15
 Printed: Dec 2015
  • Ian Charlesworth,
    Department of Mathematics, UCLA, Los Angeles, California, 90095, USA
  • Brent Nelson,
    Department of Mathematics, UCLA, Los Angeles, California, 90095, USA
  • Paul Skoufranis,
    Department of Mathematics, UCLA, Los Angeles, California, 90095, USA
Format:   LaTeX   MathJax   PDF  

Abstract

We demonstrate that the notions of bi-free independence and combinatorial-bi-free independence of two-faced families are equivalent using a diagrammatic view of bi-non-crossing partitions. These diagrams produce an operator model on a Fock space suitable for representing any two-faced family of non-commutative random variables. Furthermore, using a Kreweras complement on bi-non-crossing partitions we establish the expected formulas for the multiplicative convolution of a bi-free pair of two-faced families.
Keywords: free probability, operator algebras, bi-free free probability, operator algebras, bi-free
MSC Classifications: 46L54 show english descriptions Free probability and free operator algebras 46L54 - Free probability and free operator algebras
 

© Canadian Mathematical Society, 2018 : https://cms.math.ca/