2021/05/10 by James A. Mingo, Mingo, James A., Mihai Popa +3
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #Primary: 46L54 #Probability (math.PR) #Random Matrices and Applications #Secondary: 60B20 #Stochastic processes and statistical mechanics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2105.04076
openalex publication_date 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the effect of a partial transpose on the limit *-distribution of a Haar distributed random unitary matrix. If we fix, b, the number of blocks, we show that the partial transpose can be decomposed into a sum of b matrices which are asymptotically free and identically distributed. We then consider the joint effect of different block decompositions and show that under some mild assumptions we also get asymptotic freeness.