Archiv der Mathematik ( IF 0.518 ) Pub Date : 2021-02-22 , DOI: 10.1007/s00013-020-01569-7
Ian Charlesworth, Benoît Collins

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.

$$\ varvec {\ varepsilon}$$ε的矩阵模型-无独立性

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