On partial transposes of unitarily invariant random matrices

Abstract

We compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, it is shown the asymptotic freeness relation between the ensembles of random matrices, their transposes and their left and right partial transposes.

18 pages, small typos corrected, to appear in Int. J. Math