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I will discuss $\varepsilon$-independence, which is an interpolation of classical and free independence originally studied by Motkowski and later by Speicher and Wysoczanski. To be $\varepsilon$-independent, a family of algebras in particular must satisfy pairwise classical or free independence relations prescribed by a $\{0, 1\}$-matrix $\varepsilon$, as well as more complicated higher order relations. I will discuss how matrix models for this independence may be constructed in a suitably-chosen tensor product of matrix algebras. This is joint work with Benoit Collins.