TY - JOUR
T1 - Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection
AU - Belinschi, S. T.
AU - Popa, M.
AU - Vinnikov, V.
N1 - Funding Information:
✩ Research of S.T.B. was supported by a Discovery grant from NSERC Canada, and a University of Saskatchewan start-up grant. * Corresponding author at: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada. E-mail addresses: [email protected] (S.T. Belinschi), [email protected] (M. Popa), [email protected] (V. Vinnikov).
PY - 2012/1/1
Y1 - 2012/1/1
N2 - We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue for the Bercovici-Pata bijection. An important tool is Voiculescu's subordination property for operator-valued free convolution.
AB - We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue for the Bercovici-Pata bijection. An important tool is Voiculescu's subordination property for operator-valued free convolution.
KW - Bercovici-Pata bijection
KW - Limit theorems
KW - Non-commutative functions
KW - Operator-valued free probability
UR - http://www.scopus.com/inward/record.url?scp=80955157447&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2011.09.006
DO - 10.1016/j.jfa.2011.09.006
M3 - Article
AN - SCOPUS:80955157447
SN - 0022-1236
VL - 262
SP - 94
EP - 123
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -