%0 Journal Article
%T Star-cumulants of free unitary Brownian motion
%A Nizar Demni
%A Mathieu Guay-Paquet
%A Alexandru Nica
%J Mathematics
%D 2014
%I arXiv
%X We study joint free cumulants of u_t and u_t^{*}, where u_t 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 u_t and u_t^{*}, we "calculate the derivative" for t going to infinity, when u_t 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.
%U http://arxiv.org/abs/1408.3880v2