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arXiv · 1910.04343

Matrix models for $\varepsilon$-free independence

Ian Charlesworth·Benoît Collins
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Abstract

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 M{\l}otkowski and by Speicher and Wysocza\'nski. 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.

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Ian Charlesworth, Benoît Collins. 2019-10-10. Matrix models for $\varepsilon$-free independence. https://doi.org/10.1007/s00013-020-01569-7

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