On star-Moments of the compression of the free unitary Brownian motion by a free projection - Archive ouverte HAL Access content directly
Journal Articles Journal of Operator Theory Year : 2022

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

Nizar Demni
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• IdHAL : 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 $1/2$.

### Dates and versions

hal-03170491 , version 1 (16-03-2021)

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• HAL Id : hal-03170491 , version 1
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### Cite

Nizar Demni, Tarek Hamdi. On star-Moments of the compression of the free unitary Brownian motion by a free projection. Journal of Operator Theory, In press. ⟨hal-03170491⟩

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