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arXiv · 2001.06876

On star-Moments of the compression of the free unitary Brownian motion by a free projection

Nizar Demni·Tarek Hamdi
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Abstract

In this paper, we derive explicit expressions for the moments and for the mixed moments of the compression of a free unitary Brownian motion by a free projection. While the moments of this non-normal operator are readily derived using analytical or combinatorial methods, we only succeeded to derive its mixed ones after solving a non-linear partial differential equation for their two-variables generating function. Nonetheless, the combinatorics of non crossing partitions lead to another expression of the lowest-order mixed moment. We shall also give some interest in odd alternating moments. In particular, we derive a linear partial differential equation for their generating function and discuss the combinatorial approach to these moments when the rank of the projection equals $1/2$.

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Nizar Demni, Tarek Hamdi. 2020-01-19. On star-Moments of the compression of the free unitary Brownian motion by a free projection. https://arxiv.org/abs/2001.06876

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