Matrix models for $\epsilon$-free independence

Abstract

We investigate tensor products of random matrices, and show that independence of entries leads asymptotically to $\epsilon$-free independence, a mixture of classical and free independence studied by Młotkowski and by Speicher and Wysoczański. The particular $\epsilon$ arising is prescribed by the tensor product structure chosen, and conversely, we show that with suitable choices an arbitrary $\epsilon$ 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.

10 pages; comments welcome