Freeness and The Transposes of Unitarily Invariant Random Matrices
  We show that real second order freeness appears in the study of Haar unitary and unitarily invariant random matrices when transposes are also considered. In particular we obtain the unexpected result that a unitarily invariant random matrix will be asymptotically free from its transpose. 
James A. Mingo and Mihai Popa
math.OA math.PR