A new source for asymptotic free independence
A talk in the Seminar Zufallsmatrizen series by
Sang-Gyun Youn
| Abstract: | Free independence is at the heart of free probability, originating from a long-standing open classification problem of operator algebras. Free independence differs from the notion of independence between random variables, but it can be concretely realized by the asymptotic behavior of independent random matrices. There are many related results, and independence between random matrices is essential in obtaining free independence. A recent progress by Mingo and Popa in 2019 is the discovery of a fundamentally different approach to obtaining asymptotic freeness. They proved asymptotic freeness between the (four) partial transposes of a bipartite Wishart matrix without assuming independence between random matrices. In this talk, we explore why the partial transposition is considered important from the perspective of quantum information theory, and discuss the extendibility of this asymptotic freeness result to the general multipartite Wishart matrix and the associated free central limit theorem. Within the CRC this talk is associated to the project(s): C6 |