TY - JOUR
T1 - Star-cumulants of free unitary Brownian motion
AU - Demni, Nizar
AU - Guay-Paquet, Mathieu
AU - Nica, Alexandru
N1 - Publisher Copyright:
© 2015 Elsevier Inc. All rights reserved.
PY - 2015/8/1
Y1 - 2015/8/1
N2 - We study joint free cumulants of ut and ut∗, where ut is a free unitary Brownian motion at time t. We determine explicitly some special families of such cumulants. On the other hand, for a general joint cumulant of ut and ut∗, we "calculate the derivative" for t→∞, when ut approaches a Haar unitary. In connection to the latter calculation we put into evidence an "infinitesimal determining sequence" which naturally accompanies an arbitrary R-diagonal element in a tracial ∗-probability space.
AB - We study joint free cumulants of ut and ut∗, where ut is a free unitary Brownian motion at time t. We determine explicitly some special families of such cumulants. On the other hand, for a general joint cumulant of ut and ut∗, we "calculate the derivative" for t→∞, when ut approaches a Haar unitary. In connection to the latter calculation we put into evidence an "infinitesimal determining sequence" which naturally accompanies an arbitrary R-diagonal element in a tracial ∗-probability space.
KW - Free cumulants
KW - Free probability
KW - Free unitary Brownian motion
KW - Infinitesimal determining sequence
KW - Non-crossing partitions
KW - R-diagonal element
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U2 - 10.1016/j.aam.2015.05.001
DO - 10.1016/j.aam.2015.05.001
M3 - Article
AN - SCOPUS:84937396411
SN - 0196-8858
VL - 69
SP - 1
EP - 45
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
ER -