高维主场的矩阵逼近
Matricial approximations of higher dimensional master fields
摘要：
我们研究我们在以前的工作中构建的主域的矩阵逼近。这些近似（在非交换分布中）通过提取布朗酉扩散的块（具有$\mathbb{R}, \mathbb{C}$或$\mathbb{K}$中的条目）并使这些块的维数趋于无穷大来获得。我们将我们的研究分为两部分：在第一部分中，我们提取正方形块，而在第二部分中，我们允许矩形块。在这两种情况下，自由概率论和算子值自由概率都是最准确描述极限分布的自然框架。
英文摘要：
We study matricial approximations of master fields we constructed in a previous work. These approximations (in non-commutative distribution) are obtained by extracting blocks of a Brownian unitary diffusion (with entries in $\mathbb{R}, \mathbb{C}$ or $\mathbb{K}$) and letting the dimension of these blocks to tend to infinity. We divide our study into two parts: in the first one, we extract square blocks while in the second one we allow rectangular blocks. In both cases, free probability theory and operator-valued free probability appear as the natural framework in which the limiting distributions are most accurately described.
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