Abstract : Haagerup and Thorbjørnsen proved that iid GUEs converge strongly to free semicircular elements as the dimension grows to infinity. Motivated by considerations from quantum physics -- in particular, understanding nearest neighbor interactions in quantum spin systems -- we consider iid GUE acting on multipartite state spaces, with a mixing component on two sites and identity on the remaining sites. We show that under proper assumptions on the dimension of the sites, strong asymptotic freeness still holds. Our proof relies on an interpolation technology recently introduced by Bandeidra, Boedihardjo and van Handel. This is a joint work with Benoît Collins.

Keywords : gaussian unitary ensemble; strong asymptotic freeness; tensor