Title: Infinitesimal Freeness

Abstract: A universal rule for computing mixed moments of independent and unitarily invariant random matrices gives, in the large N limit, the rule for free independence. In the forty years since Voiculescu gave this rule many extensions and generalizations have been found.

One extension, found by Belinschi and Shlyakhtenko, is called infinitesimal freeness. This has been shown to model the case where the random matrices have different scales. I will discuss some recent joint work with Cebron, Vazquez, and Tseng.