论文标题
关于自由投影的自由统一布朗运动的恒星
On star-Moments of the compression of the free unitary Brownian motion by a free projection
论文作者
论文摘要
在本文中，我们在自由投影的自由统一布朗运动压缩的时刻和混合时刻中得出了明确的表达。尽管使用分析或组合方法很容易得出此非正态操作员的力矩，但我们仅在求解其两种变量生成函数的非线性偏微分方程后才成功得出其混合的矩。但是，非交叉分区的组合会导致最低级混合力矩的另一种表达。我们还将对奇怪的交替时刻产生兴趣。特别是，我们为其生成功能得出一个线性部分微分方程，并在投影等级等于$ 1/2 $时讨论这些时刻的组合方法。
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 $1/2$.
