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arXiv · 1408.3880

Star-cumulants of free unitary Brownian motion

Nizar Demni·Mathieu Guay-Paquet·Alexandru Nica
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Abstract

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.

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Nizar Demni, Mathieu Guay-Paquet, Alexandru Nica. 2014-08-18. Star-cumulants of free unitary Brownian motion. https://arxiv.org/abs/1408.3880

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