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Journal Articles Advances in Applied Mathematics Year : 2015

Star-cumulants of free unitary Brownian motion


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.

Dates and versions

hal-01057826 , version 1 (25-08-2014)



Nizar Demni, Mathieu Guay-Paquet, Alexandru Nica. Star-cumulants of free unitary Brownian motion. Advances in Applied Mathematics, 2015, 69, pp.1-45. ⟨10.1016/j.aam.2015.05.001⟩. ⟨hal-01057826⟩
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