Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean independent entries. More precisely, we show that, under some moment conditions, such random matrices are asymptotically [Formula: see text]-diagonal and Boolean independent from each other. This paper also gives a combinatorial condition under which such matrices are asymptotically Boolean independent from the matrix obtained by permuting the entries (thus extending a recent result in Boolean probability). In particular, we show that the random matrices considered are asymptotically Boolean independent from some of their partial transposes. The main results of the paper are based on combinatorial techniques.

中文翻译：

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具有相同分布的布尔独立项的大型矩阵的渐近性质

受最近关于具有非交换项的随机矩阵的渐近独立关系的研究的启发，我们研究了具有同分布和布尔独立项的大型矩阵的极限分布和独立关系。更准确地说，我们表明，在某些矩条件下，这样的随机矩阵是渐近的 [公式：见文本]-对角线和布尔型彼此独立。本文还给出了一个组合条件，在该条件下，这些矩阵是渐近布尔独立的，独立于通过排列条目获得的矩阵（从而扩展了布尔概率的最新结果）。特别是，我们表明所考虑的随机矩阵是渐近布尔独立的，与它们的一些部分转置无关。本文的主要结果基于组合技术。