Voiculescu's notion of asymptotic free independence applies to a wide range of random matrices, including those that are independent and unitarily invariant. In the joint work with Ion Nechita, we generalize this notion by considering random matrices with a tensor product structure that are invariant under the action of local unitary matrices. Assuming the existence of the “tensor distribution” limit described by tuples of permutations, we show that an independent family of local unitary invariant random matrices satisfies asymptotically a novel form of freeness, which we term “tensor freeness”. Furthermore, we propose a tensor free version of the central limit theorem, which extends and recovers several previous results for tensor products of free variables.
报告人简介：Dr. Park's interests lie in the mathematical aspects of Quantum Information Theory (QIT), with a focus on techniques from functional analysis and probability theory. Recently, there has been a growing trend of applying tools from operator algebras and random matrix theory to QIT, and my main interest is in contributing to this direction, particularly in entanglement theory and the study of random quantum objects.
