On Two-faced Families of Non-commutative Random Variables
Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1290-1325
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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.
Charlesworth, Ian; Nelson, Brent; Skoufranis, Paul. On Two-faced Families of Non-commutative Random Variables. Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1290-1325. doi: 10.4153/CJM-2015-002-6
@article{10_4153_CJM_2015_002_6,
author = {Charlesworth, Ian and Nelson, Brent and Skoufranis, Paul},
title = {On {Two-faced} {Families} of {Non-commutative} {Random} {Variables}},
journal = {Canadian journal of mathematics},
pages = {1290--1325},
year = {2015},
volume = {67},
number = {6},
doi = {10.4153/CJM-2015-002-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-002-6/}
}
TY - JOUR AU - Charlesworth, Ian AU - Nelson, Brent AU - Skoufranis, Paul TI - On Two-faced Families of Non-commutative Random Variables JO - Canadian journal of mathematics PY - 2015 SP - 1290 EP - 1325 VL - 67 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-002-6/ DO - 10.4153/CJM-2015-002-6 ID - 10_4153_CJM_2015_002_6 ER -
%0 Journal Article %A Charlesworth, Ian %A Nelson, Brent %A Skoufranis, Paul %T On Two-faced Families of Non-commutative Random Variables %J Canadian journal of mathematics %D 2015 %P 1290-1325 %V 67 %N 6 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-002-6/ %R 10.4153/CJM-2015-002-6 %F 10_4153_CJM_2015_002_6
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