2014/08/18 by Demni, Nizar, Guay-Paquet, Mathieu, Nica, Alexandru
#46L54 #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR)
paper · doi:10.48550/arxiv.1408.3880
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 going to infinity, 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.