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Freeness and The Partial Transposes of Wishart Random Matrices

  • James A. Mingo (a1) and Mihai Popa (a2) (a3)

We show that the partial transposes of complex Wishart random matrices are asymptotically free. We also investigate regimes where the number of blocks is fixed but the size of the blocks increases. This gives an example where the partial transpose produces freeness at the operator level. Finally, we investigate the case of real Wishart matrices.

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Research of both authors was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. Research of author M.P. was also supported by the Simons Foundation, grant No. 360242.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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