We investigate tensor products of random matrices, and show that independence of entries leads asymptotically to \(\varepsilon \)-free independence, a mixture of classical and free independence studied by Młotkowski and by Speicher and Wysoczański. The particular \(\varepsilon \) arising is prescribed by the tensor product structure chosen, and conversely, we show that with suitable choices an arbitrary \(\varepsilon \) may be realized in this way. As a result, we obtain a new proof that \(\mathcal {R}^\omega \)-embeddability is preserved under graph products of von Neumann algebras, along with an explicit recipe for constructing matrix models.

我们研究了随机矩阵的张量积，并表明条目的独立性渐近导致\（\ varepsilon \） -独立性，这是Młotkowski以及Speicher和Wysoczański研究的经典和自由独立性的混合物。所产生的特定\（\ varepsilon \）由所选的张量积结构规定，相反，我们表明，通过适当的选择，可以通过这种方式实现任意\（\ varepsilon \）。结果，我们获得了一个新的证明，即von Neumann代数的图积下\（\ mathcal {R} ^ \ omega \）可嵌入性，以及构造矩阵模型的显式方法。