Title: Norm estimates for epsilon-free semicircles

Abstract: Epsilon-freeness, studied by Speicher and Wysoczanski, is a mixture of classical and free independence characterized by a given simple graph. This independence is based on the graph product of groups introduced by Green, which was imported into operators by Caspers and Fima. For the connection with random matrices, Charlesworth and Collins constructed random matrix models whose joint moments converge to those of epsilon-free random variables. Furthermore, recent results on strong convergence for such random matrices have made the study of operator norms of epsilon-free random variables increasingly valuable.
In this talk, I will give a brief introduction to epsilon-freeness and present a joint work with Collins on operator norms for epsilon-free convolutions of semicircular random variables.