Star-cumulants of free unitary Brownian motion
Abstract
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.
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